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All questions of Understanding Quadrilaterals for Class 8 Exam
Which of the following quadrilaterals has two pairs of adjacent sides equal and diagonals intersecting at right angles?
- a)Parallelogram
- b)rhombus
- c)Triangle
- d)rectangle
Correct answer is option 'B'. Can you explain this answer?
Which of the following quadrilaterals has two pairs of adjacent sides equal and diagonals intersecting at right angles?
a)
Parallelogram
b)
rhombus
c)
Triangle
d)
rectangle
|
Pooja Shah answered |
Correct Answer :- b
Explanation:- A rhombus is a parallelogram and a quadrilateral whose opposite sides are parallel and opposite angles are equal.
Area of Rhombus, A = (d1 x d2)/2
The perimeter of Rhombus, P = 4a units
The opposite angles of a rhombus are equal to each other.
In a rhombus, diagonals bisecting each other at right angles.
Diagonals bisect the angles of a rhombus
The sides of a pentagon are produced in order. Which of the following is the sum of its exterior angles? - a)540°
- b)180°
- c)720°
- d)360°
Correct answer is option 'D'. Can you explain this answer?
The sides of a pentagon are produced in order. Which of the following is the sum of its exterior angles?
a)
540°
b)
180°
c)
720°
d)
360°
|
|
Priyanjali Singh answered |
Each polygon have 360• as it's exterior angel but it's Interior angle is depend on it's sides, so the answer is D
Which of the parallelograms has all sides equal and diagonals bisect each other at right angle?
- a)None of these
- b)rectangle
- c)rhombus
- d)trapezium.
Correct answer is option 'C'. Can you explain this answer?
Which of the parallelograms has all sides equal and diagonals bisect each other at right angle?
a)
None of these
b)
rectangle
c)
rhombus
d)
trapezium.
|
Sanjana Bose answered |
If two adjacent sides of a parallelogram are equal, then it is a rhombus.. A quadrilateral whose diagonals bisect each other at right angles is a rhombus.
In square all sides are equal and every angle is right angle.
Find the angle measure x in the following figure:
- a)90°
- b)108°
- c)120°
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
Find the angle measure x in the following figure:
a)
90°
b)
108°
c)
120°
d)
none of these
|
Ritu Joshi answered |
Angle sum of a pentagon = (5 – 2) x 180degree = 3 x 180degree =
Which of the following quadilaterals has two pairs of adjacent sides equal and diagonals intersecting at right angles?
- a)square
- b)circle
- c)rhombus
- d)rectangle.
Correct answer is option 'C'. Can you explain this answer?
Which of the following quadilaterals has two pairs of adjacent sides equal and diagonals intersecting at right angles?
a)
square
b)
circle
c)
rhombus
d)
rectangle.
|
Geetika Shah answered |
3. Rhombus
Explanation: A rhombus is a quadrilateral that has the following properties:
- All four sides are of equal length.
- It has two pairs of adjacent sides that are equal.
- The diagonals of a rhombus intersect at right angles (90 degrees) and bisect each other.
This makes the rhombus the correct answer.
- A square also has diagonals that intersect at right angles, but all four sides are equal rather than just two pairs of adjacent sides.
- A rectangle has equal opposite sides and diagonals that are equal but do not intersect at right angles.
- A circle is not a quadrilateral, so it doesn't apply to this question.
Find the value of the unknown x.
- a)80°
- b)120°
- c)100°
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Find the value of the unknown x.
a)
80°
b)
120°
c)
100°
d)
none of these
|
Shubham Sharma answered |
We have sum of adjacent angles equal to 180°, so
x + 100° = 180°
x = 80°
x + 100° = 180°
x = 80°
RICE is a rhombus. Find z.
- a)12
- b)13
- c)5
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
RICE is a rhombus. Find z.
a)
12
b)
13
c)
5
d)
none of these
|
Amit Sharma answered |
Given a rhombus RICE where
RE = 13, Ol = 5 OC = 12
In a rhombus,
Diagonals bisect each other
Also,
All sides of a rhombus are equal.
RI = RE
z = 13
∴ x = 5, y = 12 and z =13
RE = 13, Ol = 5 OC = 12
In a rhombus,
Diagonals bisect each other
Also,
All sides of a rhombus are equal.
RI = RE
z = 13
∴ x = 5, y = 12 and z =13
The ________ of a rhombus are perpendicular bisectors of one another.- a)angles
- b)sides
- c)diagonals
- d)none of these
Correct answer is 'C'. Can you explain this answer?
The ________ of a rhombus are perpendicular bisectors of one another.
a)
angles
b)
sides
c)
diagonals
d)
none of these
|
Rajveer Goyal answered |
Explanation:
A rhombus is a quadrilateral with all sides equal in length. It is also known as a diamond shape. The diagonals of a rhombus are the line segments that connect opposite vertices of the rhombus.
The diagonals of a rhombus have some important properties:
1. The diagonals of a rhombus bisect each other at right angles. This means that the point where the diagonals intersect is the midpoint of each diagonal, and the diagonals form four right angles.
2. The diagonals of a rhombus are equal in length. This is because a rhombus has four sides of equal length, and the diagonals connect opposite vertices, which are also equidistant from the center of the rhombus.
3. The diagonals of a rhombus are perpendicular bisectors of each other. This means that each diagonal divides the other diagonal into two equal parts, and each diagonal is perpendicular to the other diagonal.
Therefore, we can conclude that the correct answer is option C, which states that the diagonals of a rhombus are perpendicular bisectors of each other.
A rhombus is a quadrilateral with all sides equal in length. It is also known as a diamond shape. The diagonals of a rhombus are the line segments that connect opposite vertices of the rhombus.
The diagonals of a rhombus have some important properties:
1. The diagonals of a rhombus bisect each other at right angles. This means that the point where the diagonals intersect is the midpoint of each diagonal, and the diagonals form four right angles.
2. The diagonals of a rhombus are equal in length. This is because a rhombus has four sides of equal length, and the diagonals connect opposite vertices, which are also equidistant from the center of the rhombus.
3. The diagonals of a rhombus are perpendicular bisectors of each other. This means that each diagonal divides the other diagonal into two equal parts, and each diagonal is perpendicular to the other diagonal.
Therefore, we can conclude that the correct answer is option C, which states that the diagonals of a rhombus are perpendicular bisectors of each other.
In a parallelogram, opposite sides are:
- a)Unequal and parallel
- b)Equal and perpendicular
- c)Equal and parallel
- d)Unequal and perpendicular
Correct answer is option 'C'. Can you explain this answer?
In a parallelogram, opposite sides are:
a)
Unequal and parallel
b)
Equal and perpendicular
c)
Equal and parallel
d)
Unequal and perpendicular
|
Vivek Rana answered |
- Equal: Opposite sides of a parallelogram have the same length.
- Parallel: Opposite sides of a parallelogram run parallel to each other.
These properties ensure that the figure maintains its shape and symmetry, characteristic of parallelograms. Therefore, the correct answer is C: Equal and parallel.
- Parallel: Opposite sides of a parallelogram run parallel to each other.
These properties ensure that the figure maintains its shape and symmetry, characteristic of parallelograms. Therefore, the correct answer is C: Equal and parallel.
A simple closed curve made up of only line segments is called a ________.- a)polygon
- b)quadrilateral
- c)hexagon
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
A simple closed curve made up of only line segments is called a ________.
a)
polygon
b)
quadrilateral
c)
hexagon
d)
none of these
|
|
Illusion Hell answered |
(A) option (the curve made up of line segments).
- a)45°
- b)120°
- c)140°
- d)none of these
Correct answer is 'C'. Can you explain this answer?
a)
45°
b)
120°
c)
140°
d)
none of these
|
Gungun Shrivas answered |
Sum of all angles of a quadrilateral is 360 degree . so we will add all the angles of quadrilateral and subtract it from 360 to get x. there is a linear pair on left side and exterior angle is 90 hence the other angle will be 90 by linear pair property. hence 70+60+90+x=360 220+x=360 x=360-220 x=140 hence C is the right answer.
Find the measure of each exterior angle of a regular polygon of 9 sides.- a)30°
- b)90°
- c)40°
- d)60°
Correct answer is option 'C'. Can you explain this answer?
Find the measure of each exterior angle of a regular polygon of 9 sides.
a)
30°
b)
90°
c)
40°
d)
60°
|
|
Sanjana Bose answered |
Sum of all exterior angles of the given polygon = 360degree
Each exterior angle of a regular polygon has the same measure.
Thus, measure of each exterior angle of a regular polygon of 9 sides=360/9= 40degree.
A _________ has all the properties of a parallelogram and also that of a kite.- a)rhombus
- b)quadrilateral
- c)parallelogram
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
A _________ has all the properties of a parallelogram and also that of a kite.
a)
rhombus
b)
quadrilateral
c)
parallelogram
d)
none of these
|
Anisha Sharma answered |
A rhombus has all the properties of a parallelogram and also that of a kite. Let's break down the properties of each shape to understand why a rhombus fits the description.
**Properties of a Parallelogram:**
1. Opposite sides are parallel: In a parallelogram, opposite sides are always parallel. This means that if you extend the sides of a parallelogram, they will never intersect.
2. Opposite sides are congruent: The lengths of opposite sides in a parallelogram are equal. This implies that if you measure the length of one side and compare it to the length of the opposite side, they will be the same.
3. Opposite angles are congruent: The angles formed by the intersection of the sides in a parallelogram are equal. If you measure one angle and compare it to the angle opposite it, they will have the same measure.
4. Consecutive angles are supplementary: The sum of two consecutive angles in a parallelogram is always 180 degrees. For example, if angle A and angle B are consecutive angles in a parallelogram, then angle A + angle B = 180 degrees.
**Properties of a Kite:**
1. Two pairs of adjacent sides are congruent: In a kite, two consecutive sides are equal in length. This means that if you measure the length of one side and compare it to the length of the side next to it, they will be the same.
2. One pair of opposite angles is congruent: The angles formed by the intersection of the sides in a kite are equal. If you measure one angle and compare it to the angle opposite it, they will have the same measure.
3. Diagonals are perpendicular: The diagonals of a kite are perpendicular to each other. This means that if you draw the diagonals of a kite, they will intersect at a right angle.
Based on these properties, a rhombus fits the description of having all the properties of a parallelogram and also that of a kite.
In a rhombus:
- Opposite sides are parallel (parallelogram property).
- Opposite sides are congruent (parallelogram property).
- Opposite angles are congruent (parallelogram property).
- Consecutive angles are supplementary (parallelogram property).
- Two pairs of adjacent sides are congruent (kite property).
- One pair of opposite angles is congruent (kite property).
- Diagonals are perpendicular (kite property).
Therefore, a rhombus is the correct answer as it encompasses all the properties of both a parallelogram and a kite.
**Properties of a Parallelogram:**
1. Opposite sides are parallel: In a parallelogram, opposite sides are always parallel. This means that if you extend the sides of a parallelogram, they will never intersect.
2. Opposite sides are congruent: The lengths of opposite sides in a parallelogram are equal. This implies that if you measure the length of one side and compare it to the length of the opposite side, they will be the same.
3. Opposite angles are congruent: The angles formed by the intersection of the sides in a parallelogram are equal. If you measure one angle and compare it to the angle opposite it, they will have the same measure.
4. Consecutive angles are supplementary: The sum of two consecutive angles in a parallelogram is always 180 degrees. For example, if angle A and angle B are consecutive angles in a parallelogram, then angle A + angle B = 180 degrees.
**Properties of a Kite:**
1. Two pairs of adjacent sides are congruent: In a kite, two consecutive sides are equal in length. This means that if you measure the length of one side and compare it to the length of the side next to it, they will be the same.
2. One pair of opposite angles is congruent: The angles formed by the intersection of the sides in a kite are equal. If you measure one angle and compare it to the angle opposite it, they will have the same measure.
3. Diagonals are perpendicular: The diagonals of a kite are perpendicular to each other. This means that if you draw the diagonals of a kite, they will intersect at a right angle.
Based on these properties, a rhombus fits the description of having all the properties of a parallelogram and also that of a kite.
In a rhombus:
- Opposite sides are parallel (parallelogram property).
- Opposite sides are congruent (parallelogram property).
- Opposite angles are congruent (parallelogram property).
- Consecutive angles are supplementary (parallelogram property).
- Two pairs of adjacent sides are congruent (kite property).
- One pair of opposite angles is congruent (kite property).
- Diagonals are perpendicular (kite property).
Therefore, a rhombus is the correct answer as it encompasses all the properties of both a parallelogram and a kite.
Which of the following quadrilaterals has two pairs of adjacent sides equal and diagonals intersecting at right angles?
- a)parallelogram
- b)kite
- c)rectangle
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
Which of the following quadrilaterals has two pairs of adjacent sides equal and diagonals intersecting at right angles?
a)
parallelogram
b)
kite
c)
rectangle
d)
None of these
|
Sounak Sengupta answered |
Kite, is a quadrilaterals has two pairs of adjacent sides equal and diagonals intersecting at right angles.
The opposite sides of a parallelogram are of ________ length.- a)not equal
- b)different
- c)equal
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
The opposite sides of a parallelogram are of ________ length.
a)
not equal
b)
different
c)
equal
d)
none of these
|
|
Shubham Sharma answered |
It’s a property of parallelogram that opposite sides of a parallelogram are equal and parallel.
RICE is a rhombus. Find x.
- a)5
- b)12
- c)13
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
RICE is a rhombus. Find x.
a)
5
b)
12
c)
13
d)
none of these
|
|
Ananya Das answered |
Given a rhombus RICE where
RE = 13, Ol = 5 OC = 12
In a rhombus,
Diagonals bisect each other
Also,
All sides of a rhombus are equal.
RI = RE
x = 5
∴ x = 5, y = 12 and z =13
RE = 13, Ol = 5 OC = 12
In a rhombus,
Diagonals bisect each other
Also,
All sides of a rhombus are equal.
RI = RE
x = 5
∴ x = 5, y = 12 and z =13
What do you call a parallelogram which has equal diagonals?
- a)A trapezium
- b)A rectangle
- c)A rhombus
- d)A kite
Correct answer is option 'B'. Can you explain this answer?
What do you call a parallelogram which has equal diagonals?
a)
A trapezium
b)
A rectangle
c)
A rhombus
d)
A kite
|
C K Academy answered |
A parallelogram which has equal diagonals are called rectangle. Trapezium, rhombus and kite does not contain equal diagonal.
Proof for rectangle contains equal diagonals are given below :-
Proof for rectangle contains equal diagonals are given below :-
⇒ In given figure ABCD is a rectangle.
⇒ In △ABC and △DCB
⇒ BC = CB [Common]
⇒ AB = DC [Opposite sides of rectangle]
⇒ ∠ABC = ∠DCA = 90∘ [Each angle of rectangle is 90∘]
⇒ △ABC ≅ △DCB [By SAS property]
∴ AC = BD [By CPCT]
The diagonal of a rectangle is 10 cm and its breadth is6 cm. What is its length?- a)6 cm
- b)5cm
- c)8cm
- d)4cm
Correct answer is option 'C'. Can you explain this answer?
The diagonal of a rectangle is 10 cm and its breadth is6 cm. What is its length?
a)
6 cm
b)
5cm
c)
8cm
d)
4cm
|
|
Shubham Sharma answered |
Apply Pythagoras Theorem,
(Diagonal)2 = (Breadth)2 + (Length)2
100 = 36+(Length)2
Length=8cm
(Diagonal)2 = (Breadth)2 + (Length)2
100 = 36+(Length)2
Length=8cm
Find the value of the unknown z.
- a)130°
- b)150°
- c)180°
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
Find the value of the unknown z.
a)
130°
b)
150°
c)
180°
d)
none of these
|
|
Lakshita Meena answered |
50+y=180
y=180-50=130
x+130=180
x=180-130=50
z=50 (Vertically opposite angles are equal)
How many diagonals does a triangle have?- a)2
- b)1
- c)0
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
How many diagonals does a triangle have?
a)
2
b)
1
c)
0
d)
None of these
|
Prateek Ghoshal answered |
Explanation:
A diagonal is a line segment that connects two nonadjacent vertices of a polygon. In the case of a triangle, a diagonal would connect two vertices that are not adjacent to each other.
A triangle has three sides and three vertices. Let's label the vertices as A, B, and C.
To count the number of diagonals, we need to connect each vertex to every other vertex that is not adjacent to it.
Connecting vertex A:
- A cannot be connected to itself, so we eliminate one possibility.
- A can be connected to B, which forms one diagonal.
- A can be connected to C, which forms another diagonal.
Connecting vertex B:
- B cannot be connected to itself, so we eliminate one possibility.
- B can be connected to A, which forms one diagonal.
- B can be connected to C, which forms another diagonal.
Connecting vertex C:
- C cannot be connected to itself, so we eliminate one possibility.
- C can be connected to A, which forms one diagonal.
- C can be connected to B, which forms another diagonal.
Total number of diagonals:
Adding up all the possibilities, we have a total of 2 + 2 + 2 = 6 diagonals.
However, we need to remember that a diagonal must connect two nonadjacent vertices. In a triangle, all the vertices are adjacent to each other. Therefore, no diagonals can be formed within a triangle.
Hence, the correct answer is option C: 0 diagonals.
A diagonal is a line segment that connects two nonadjacent vertices of a polygon. In the case of a triangle, a diagonal would connect two vertices that are not adjacent to each other.
A triangle has three sides and three vertices. Let's label the vertices as A, B, and C.
To count the number of diagonals, we need to connect each vertex to every other vertex that is not adjacent to it.
Connecting vertex A:
- A cannot be connected to itself, so we eliminate one possibility.
- A can be connected to B, which forms one diagonal.
- A can be connected to C, which forms another diagonal.
Connecting vertex B:
- B cannot be connected to itself, so we eliminate one possibility.
- B can be connected to A, which forms one diagonal.
- B can be connected to C, which forms another diagonal.
Connecting vertex C:
- C cannot be connected to itself, so we eliminate one possibility.
- C can be connected to A, which forms one diagonal.
- C can be connected to B, which forms another diagonal.
Total number of diagonals:
Adding up all the possibilities, we have a total of 2 + 2 + 2 = 6 diagonals.
However, we need to remember that a diagonal must connect two nonadjacent vertices. In a triangle, all the vertices are adjacent to each other. Therefore, no diagonals can be formed within a triangle.
Hence, the correct answer is option C: 0 diagonals.
In the figure, ABCD is a parallelogram.
Find the respective values of x, y and z.- a)100o, 80o, 100o
- b)100o, 100o, 80o
- c)80o, 100o, 100o
- d)80o, 80o,100o
Correct answer is option 'B'. Can you explain this answer?
In the figure, ABCD is a parallelogram.
Find the respective values of x, y and z.
a)
100o, 80o, 100o
b)
100o, 100o, 80o
c)
80o, 100o, 100o
d)
80o, 80o,100o
|
Aniket Choudhary answered |
C is opposite to A. So,
x = 100o (Opposite angles property.)
y = 100o (Measure of angle corresponding to ∠x.)
z = 80o (Since ∠y,∠z is a linear pair)
x = 100o (Opposite angles property.)
y = 100o (Measure of angle corresponding to ∠x.)
z = 80o (Since ∠y,∠z is a linear pair)
In the quadrilateral ABCD, the diagonals AC and BD are equal and perpendicular to each other. What type of a quadrilateral is ABCD?- a)A square
- b)A parallelogram
- c)A rhombus
- d)A trapezium
Correct answer is option 'A'. Can you explain this answer?
In the quadrilateral ABCD, the diagonals AC and BD are equal and perpendicular to each other. What type of a quadrilateral is ABCD?
a)
A square
b)
A parallelogram
c)
A rhombus
d)
A trapezium
|
Saranya Khanna answered |
A quadrilateral in which the diagonals are equal and perpendicular is called a square.
If angles P, Q, R and S of the quadrilateral PQRS, taken in order, are in the ratio 3:7:6:4, what is PQRS?- a)A rhombus
- b)A parallelogram
- c)A trapezium
- d)A kite
Correct answer is option 'C'. Can you explain this answer?
If angles P, Q, R and S of the quadrilateral PQRS, taken in order, are in the ratio 3:7:6:4, what is PQRS?
a)
A rhombus
b)
A parallelogram
c)
A trapezium
d)
A kite
|
Mansi Tiwari answered |
Let the angles be 3x, 7x , 6x and 4x.
∴ 3x+7x+6x+4x = 360o or 20x = 360o or x = 18o.
The angles are 54o,126o,108o and 72o.
We see that adjacent angles are supplementary but opposite angles-are not equal. Clearly, it is a trapezium.
∴ 3x+7x+6x+4x = 360o or 20x = 360o or x = 18o.
The angles are 54o,126o,108o and 72o.
We see that adjacent angles are supplementary but opposite angles-are not equal. Clearly, it is a trapezium.
In a parallelogram ABCD, if AB = 2x+5,CD = y+1, AD= y+5 and BC = 3x−4,what is the ratio of AB and BC?- a)71:21
- b)12:11
- c)31:35
- d)4:7
Correct answer is option 'C'. Can you explain this answer?
In a parallelogram ABCD, if AB = 2x+5,CD = y+1, AD= y+5 and BC = 3x−4,what is the ratio of AB and BC?
a)
71:21
b)
12:11
c)
31:35
d)
4:7
|
|
Pritam Ghoshal answered |
In a parallelogram, opposite sides are equal in length.
Therefore, AB = CD and AD = BC.
Given that AB = 2x + 5, CD = y + 1, AD = y + 5, and BC = 3x, we can set up two equations:
2x + 5 = y + 1 (equation 1)
y + 5 = 3x (equation 2)
From equation 1, we can isolate y:
y = 2x + 4
Substituting this value of y into equation 2, we get:
2x + 4 + 5 = 3x
Simplifying, we have:
9 = x
Now we can substitute this value of x back into the equations to find the lengths of the sides:
AB = 2(9) + 5 = 23
CD = y + 1 = (2(9) + 4) + 1 = 23
AD = y + 5 = (2(9) + 4) + 5 = 27
BC = 3(9) = 27
So, the lengths of the sides are AB = 23, CD = 23, AD = 27, and BC = 27.
Therefore, AB = CD and AD = BC.
Given that AB = 2x + 5, CD = y + 1, AD = y + 5, and BC = 3x, we can set up two equations:
2x + 5 = y + 1 (equation 1)
y + 5 = 3x (equation 2)
From equation 1, we can isolate y:
y = 2x + 4
Substituting this value of y into equation 2, we get:
2x + 4 + 5 = 3x
Simplifying, we have:
9 = x
Now we can substitute this value of x back into the equations to find the lengths of the sides:
AB = 2(9) + 5 = 23
CD = y + 1 = (2(9) + 4) + 1 = 23
AD = y + 5 = (2(9) + 4) + 5 = 27
BC = 3(9) = 27
So, the lengths of the sides are AB = 23, CD = 23, AD = 27, and BC = 27.
In the figure, ABCD is a rhombus and ABDE is a parallelogram.
Given that EDC is a straight line and ∠AED = 36o find ∠BAD.- a)36o
- b)72o
- c)108o
- d)120o
Correct answer is option 'C'. Can you explain this answer?
In the figure, ABCD is a rhombus and ABDE is a parallelogram.
Given that EDC is a straight line and ∠AED = 36o find ∠BAD.
a)
36o
b)
72o
c)
108o
d)
120o
|
|
Saranya Khanna answered |
BDC = AED = 36o (Corresponding s, AE BD.) ABD= BDC = 36o (Alternate s, AB DC) ADB = ABD = 36o (Base angles of isosceles, since AB = DC) BAD = 180o−ABD−ADB (Angle sum of a triangle.) = 180o−36o−36o = 108o
If ABCD is an isosceles trapezium, what is the measure of ∠C?- a)∠B
- b)∠A
- c)∠D
- d)90o
Correct answer is option 'C'. Can you explain this answer?
If ABCD is an isosceles trapezium, what is the measure of ∠C?
a)
∠B
b)
∠A
c)
∠D
d)
90o
|
Pankaj Unni answered |
From definition, we know that in an isosceles trapezium the non-parallel sides are equal or AD = BC in the figure. Drop perpendiculars AE and BF to CD. Triangles AED and BFC are congruent by R.H.S congruency. Hence, ∠D = ∠C
If two adjacent angles of a parallelogram are in the ratio 3:2, what are their measures?- a)108o, 72o
- b)72o, 36o
- c)100o, 80o
- d)144o, 36o
Correct answer is option 'A'. Can you explain this answer?
If two adjacent angles of a parallelogram are in the ratio 3:2, what are their measures?
a)
108o, 72o
b)
72o, 36o
c)
100o, 80o
d)
144o, 36o
|
Sankar Datta answered |
Let the angles be 3x and 2x. We have, 3x+2x = 180o ⇒ 5x = 180o ⇒ x = 36o
∴ The angles are 36o×3 and 36o×2 = 108o and 72o.
∴ The angles are 36o×3 and 36o×2 = 108o and 72o.
A diagonal of a rectangle is inclined to one side of the rectangle at 25o. What is the measure of the acute angle between the diagonals?- a)25o
- b)40o
- c)50o
- d)55o
Correct answer is option 'C'. Can you explain this answer?
A diagonal of a rectangle is inclined to one side of the rectangle at 25o. What is the measure of the acute angle between the diagonals?
a)
25o
b)
40o
c)
50o
d)
55o
|
Shreya Bajaj answered |
Since ∠CAB = 25o ∠CAB = 65o
Let diagonals meet at O. ΔOCB is an isosceles triangle.
∴ ∠OBC = 65o
⇒ ∠BOC = 50o
State the name of a regular polygon of 6 sides.- a)pentagon
- b)hexagon
- c)heptagon
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
State the name of a regular polygon of 6 sides.
a)
pentagon
b)
hexagon
c)
heptagon
d)
none of these
|
|
R.k. Navydita answered |
A) Pentagon have 5 sides
B) Hexagon have 6 sides
C) Heptagon have 7 sides
So the correct answer is B.
In a square ABCD, the diagonals bisect at O. What type of a triangle is AOB?- a)An equilateral triangle.
- b)An isosceles but not a right angled triangle.
- c)A right angled but not an isosceles triangle.
- d)An isosceles right angled triangle.
Correct answer is option 'D'. Can you explain this answer?
In a square ABCD, the diagonals bisect at O. What type of a triangle is AOB?
a)
An equilateral triangle.
b)
An isosceles but not a right angled triangle.
c)
A right angled but not an isosceles triangle.
d)
An isosceles right angled triangle.
|
Ritika Basak answered |
Since diagonals of a square are equal and bisect at right angles, triangle AOB is an isosceles right angled triangle.
If the sides of a quadrilateral are produced in order, what is the sum of the exterior angles so formed?- a)
- 360°
- b)
- 540°
- c)
- 720°
- d)
- 900°
Correct answer is option 'A'. Can you explain this answer?
If the sides of a quadrilateral are produced in order, what is the sum of the exterior angles so formed?
a)
b)
c)
d)
|
Coders Trust answered |
When the sides of a quadrilateral are extended, each exterior angle is the supplementary angle to its interior angle. The sum of the exterior angles of any convex polygon is always 360° because each exterior angle represents a turn around the shape, and all turns together make one full circle. Hence, the sum of the exterior angles of a quadrilateral is 360°.
How many diagonals does a rectangle have?- a)2
- b)1
- c)0
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
How many diagonals does a rectangle have?
a)
2
b)
1
c)
0
d)
none of these
|
|
Anushka Shah answered |
Diagonals in a Rectangle
A rectangle is a four-sided polygon with opposite sides that are equal in length and four right angles. Diagonals are line segments that connect two nonadjacent vertices of a polygon. In the case of a rectangle, the diagonals connect the opposite corners or vertices of the rectangle.
Calculating the Number of Diagonals
To determine the number of diagonals in a rectangle, we need to consider the number of possible pairs of nonadjacent vertices. In a rectangle, there are two pairs of opposite vertices. Let's examine each pair separately.
1. Pair of Opposite Vertices on the Longer Side:
- The longer side of a rectangle is also known as its length.
- Let's assume the length of the rectangle is 'L'.
- The longer side has two opposite vertices.
- These two vertices can be connected by a diagonal.
- Therefore, there is 1 diagonal formed by this pair of vertices.
2. Pair of Opposite Vertices on the Shorter Side:
- The shorter side of a rectangle is also known as its width.
- Let's assume the width of the rectangle is 'W'.
- The shorter side has two opposite vertices.
- These two vertices can also be connected by a diagonal.
- Therefore, there is 1 diagonal formed by this pair of vertices.
Total Number of Diagonals
By adding up the number of diagonals formed by each pair of opposite vertices, we can determine the total number of diagonals in a rectangle.
In this case, we have:
- 1 diagonal formed by the pair of opposite vertices on the longer side.
- 1 diagonal formed by the pair of opposite vertices on the shorter side.
Therefore, a rectangle has a total of 2 diagonals.
Conclusion
To summarize, a rectangle has two diagonals. One diagonal is formed by a pair of opposite vertices on the longer side, while the other diagonal is formed by a pair of opposite vertices on the shorter side.
A rectangle is a four-sided polygon with opposite sides that are equal in length and four right angles. Diagonals are line segments that connect two nonadjacent vertices of a polygon. In the case of a rectangle, the diagonals connect the opposite corners or vertices of the rectangle.
Calculating the Number of Diagonals
To determine the number of diagonals in a rectangle, we need to consider the number of possible pairs of nonadjacent vertices. In a rectangle, there are two pairs of opposite vertices. Let's examine each pair separately.
1. Pair of Opposite Vertices on the Longer Side:
- The longer side of a rectangle is also known as its length.
- Let's assume the length of the rectangle is 'L'.
- The longer side has two opposite vertices.
- These two vertices can be connected by a diagonal.
- Therefore, there is 1 diagonal formed by this pair of vertices.
2. Pair of Opposite Vertices on the Shorter Side:
- The shorter side of a rectangle is also known as its width.
- Let's assume the width of the rectangle is 'W'.
- The shorter side has two opposite vertices.
- These two vertices can also be connected by a diagonal.
- Therefore, there is 1 diagonal formed by this pair of vertices.
Total Number of Diagonals
By adding up the number of diagonals formed by each pair of opposite vertices, we can determine the total number of diagonals in a rectangle.
In this case, we have:
- 1 diagonal formed by the pair of opposite vertices on the longer side.
- 1 diagonal formed by the pair of opposite vertices on the shorter side.
Therefore, a rectangle has a total of 2 diagonals.
Conclusion
To summarize, a rectangle has two diagonals. One diagonal is formed by a pair of opposite vertices on the longer side, while the other diagonal is formed by a pair of opposite vertices on the shorter side.
Find the number of sides of a regular polygon whose each exterior angle has a measure of 450- a)6
- b)3
- c)4
- d)8
Correct answer is 'D'. Can you explain this answer?
Find the number of sides of a regular polygon whose each exterior angle has a measure of 450
a)
6
b)
3
c)
4
d)
8
|
Ashwin Jain answered |
Sum of the exterior angles of regular polygon = 360degree
But each exterior angle = 45degree
number of sides of regular polygon = 360degree/ 45degree = 8.
If AB and CD are diameters, what is ACBD?
- a)A square
- b)A trapezium
- c)An isosceles trapezium
- d)A rectangle
Correct answer is option 'D'. Can you explain this answer?
If AB and CD are diameters, what is ACBD?
a)
A square
b)
A trapezium
c)
An isosceles trapezium
d)
A rectangle
|
Dipika Mukherjee answered |
Since the angle in a semicircle is a right angle, clearly ∠A = ∠C = ∠B = ∠D = 90o
The diagonals (diameters) are equal but they are not intersecting (bisecting) at right angles. Hence, it is not a square and can be only a rectangle.
The diagonals (diameters) are equal but they are not intersecting (bisecting) at right angles. Hence, it is not a square and can be only a rectangle.
A _________ is a quadrilateral whose opposite sides are parallel.- a)rhombus
- b)parallelogram
- c)quadrilateral
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
A _________ is a quadrilateral whose opposite sides are parallel.
a)
rhombus
b)
parallelogram
c)
quadrilateral
d)
none of these
|
Sushant Menon answered |
Definition of a Parallelogram:
A parallelogram is a quadrilateral in which opposite sides are parallel and congruent. In other words, a parallelogram is a quadrilateral with two pairs of parallel sides.
Properties of a Parallelogram:
- Opposite sides are congruent
- Opposite angles are congruent
- Consecutive angles are supplementary
- Diagonals bisect each other
- The sum of the squares of the lengths of its sides is equal to the sum of the squares of the lengths of its diagonals.
Examples of Parallelograms:
- Rectangle: A parallelogram in which all angles are right angles.
- Rhombus: A parallelogram in which all sides are congruent.
- Square: A parallelogram in which all sides are congruent and all angles are right angles.
- Trapezoid: A quadrilateral with one pair of parallel sides.
Conclusion:
A parallelogram is a special type of quadrilateral in which opposite sides are parallel. It has many properties that make it useful in geometry and other areas of mathematics. Some examples of parallelograms include rectangles, rhombuses, squares, and trapezoids.
A parallelogram is a quadrilateral in which opposite sides are parallel and congruent. In other words, a parallelogram is a quadrilateral with two pairs of parallel sides.
Properties of a Parallelogram:
- Opposite sides are congruent
- Opposite angles are congruent
- Consecutive angles are supplementary
- Diagonals bisect each other
- The sum of the squares of the lengths of its sides is equal to the sum of the squares of the lengths of its diagonals.
Examples of Parallelograms:
- Rectangle: A parallelogram in which all angles are right angles.
- Rhombus: A parallelogram in which all sides are congruent.
- Square: A parallelogram in which all sides are congruent and all angles are right angles.
- Trapezoid: A quadrilateral with one pair of parallel sides.
Conclusion:
A parallelogram is a special type of quadrilateral in which opposite sides are parallel. It has many properties that make it useful in geometry and other areas of mathematics. Some examples of parallelograms include rectangles, rhombuses, squares, and trapezoids.
Chapter doubts & questions for Understanding Quadrilaterals - Mathematics (Maths) Class 8 2025 is part of Class 8 exam preparation. The chapters have been prepared according to the Class 8 exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Class 8 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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