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All questions of The Triangles and its properties for Class 7 Exam
A triangle in which two sides are of equal lengths is called _______________.- a)scalene
- b)acute-angled
- c)equilateral
- d)isosceles
Correct answer is option 'D'. Can you explain this answer?
A triangle in which two sides are of equal lengths is called _______________.
a)
scalene
b)
acute-angled
c)
equilateral
d)
isosceles
|
Praveen Kumar answered |
AB is the hypotenuse ⇒ C has the right angle.
- a)50°
- b)120°
- c)110°
- d)30°
Correct answer is 'A'. Can you explain this answer?
a)
50°
b)
120°
c)
110°
d)
30°
|
Vrinda Maheshwari answered |
Exterior angle is equal to opposite interior angle so, when we add 50 degree to 30 it will come 80 degree .. that 'A' is correct
The altitude and median be same for a which triangle?
- a)Scalene triangle
- b)Equilateral triangle
- c)Acute
- d)Right
Correct answer is option 'B'. Can you explain this answer?
The altitude and median be same for a which triangle?
a)
Scalene triangle
b)
Equilateral triangle
c)
Acute
d)
Right
|
Sparsh Khanna answered |
In an equilateral triangle, both the median and the altitude are the same. This is because the perpendicular line drawn from the vertex of the triangle to the base cuts it equally. Also in the isosceles triangle, altitude and median are the same.
What is the measure of angle x ?
- a)30°
- b)40°
- c)25°
- d)60°
Correct answer is option 'B'. Can you explain this answer?
What is the measure of angle x ?
a)
30°
b)
40°
c)
25°
d)
60°
|
Rainbow Rise Classes answered |
if in a triangle 2 sides are equal then the angles would also be equal
x = 40ο
x = 40ο
The triangle whose lengths of sides are 3 cm, 4 cm, 5 cm is a
- a)obtuse-angled triangle
- b)right-angled triangle
- c)acute-angled triangle
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
The triangle whose lengths of sides are 3 cm, 4 cm, 5 cm is a
a)
obtuse-angled triangle
b)
right-angled triangle
c)
acute-angled triangle
d)
None of these
|
|
Sparsh Khanna answered |
a2+b2=c2
we find 32+42=52
9 + 16 = 25
as pythogoreus theorem can be applied
So, these sides also cause it to be a right triangle.
Find the value of x.
- a)110°
- b)60°
- c)70°
- d)50°
Correct answer is option 'B'. Can you explain this answer?
Find the value of x.
a)
110°
b)
60°
c)
70°
d)
50°
|
Rohini Seth answered |
An exterior angle of a triangle is equal to the sum of the opposite interior angles
So in the given figure
110o = 50o + x
110o - 50o = x
60o = x
So option B is correct answer.
Can you explain the answer of this question below:How many medians a triangle can have?A:1B:2C:3D:none of theseThe answer is C.
|
Sneha Khanna answered |
In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid.
How many altitude can a triangle have?- a)1
- b)2
- c)3
- d)None of these
Correct answer is 'C'. Can you explain this answer?
How many altitude can a triangle have?
a)
1
b)
2
c)
3
d)
None of these
|
Anshul Rane answered |
A triangle can have 3 altitudes
- a)60°
- b)50°
- c)120°
- d)70°
Correct answer is option 'C'. Can you explain this answer?
a)
60°
b)
50°
c)
120°
d)
70°
|
Rahul Shah answered |
An exterior angle of a triangle is equal to the sum of the opposite interior angles
x deg = 70 deg + 50 deg
x deg = 120 deg .
So option C is the correct answer.
- a)median
- b)side
- c)altitude
- d)bisector
Correct answer is option 'C'. Can you explain this answer?
a)
median
b)
side
c)
altitude
d)
bisector
|
Lavanya Menon answered |
In Δ PQR, PM is altitude
ΔABC is right-angled at C. If AC = 5 cm and BC = 12 cm find the length of AB.
- a)13 cm
- b)11 cm
- c)20 cm
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
ΔABC is right-angled at C. If AC = 5 cm and BC = 12 cm find the length of AB.
a)
13 cm
b)
11 cm
c)
20 cm
d)
None of these
|
Tutorpedia Coaching answered |
By Pythagoras property,
AB2 = AC2 + BC2
= 52 + 122 = 25 + 144 = 169 = 132
or AB2= 132. So, AB = 13 or the length of AB is 13 cm.
AB2 = AC2 + BC2
= 52 + 122 = 25 + 144 = 169 = 132
or AB2= 132. So, AB = 13 or the length of AB is 13 cm.
A/an _____________ connect a vertex of a triangle to the mid-point of the opposite side.- a)altitude
- b)median
- c)vertex
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
A/an _____________ connect a vertex of a triangle to the mid-point of the opposite side.
a)
altitude
b)
median
c)
vertex
d)
None of these
|
Anita Menon answered |
A/an median connect a vertex of a triangle to the mid-point of the opposite side.
In ΔPQR, PD is
- a)Altitude
- b)Bisector
- c)side
- d)Median
Correct answer is option 'D'. Can you explain this answer?
In ΔPQR, PD is
a)
Altitude
b)
Bisector
c)
side
d)
Median
|
Priyanka Sharma answered |
Median is a line joining the vertex and middle of the opposite side, and hence dividing the triangle in two equal parts. So PD is the median.
- a)50°
- b)60°
- c)180°
- d)120°
Correct answer is option 'B'. Can you explain this answer?
a)
50°
b)
60°
c)
180°
d)
120°
|
|
Priyanka Sharma answered |
Exterior angle is equal to sum of interior opposite angles so,
120 = 60+x
x = 60°
120 = 60+x
x = 60°
ΔPQR is a triangle right-angled at P. If PQ = 3 cm and PR = 4 cm, find QR.- a)8 cm
- b)5 cm
- c)7 cm
- d)3 cm
Correct answer is option 'B'. Can you explain this answer?
ΔPQR is a triangle right-angled at P. If PQ = 3 cm and PR = 4 cm, find QR.
a)
8 cm
b)
5 cm
c)
7 cm
d)
3 cm
|
|
Anita Menon answered |
Using pythagoras theorem,
QR2 = PR2 + PQ2
42+32
=16+9=25
QR = 5cm
QR2 = PR2 + PQ2
42+32
=16+9=25
QR = 5cm
One of the angles of a triangle is 110 degree and the other two angles are equal what is the measure of each of these equal angles- a)35 deg,35 deg
- b)40deg , 40deg
- c)11deg, 11 deg
- d)80deg , 80 deg
Correct answer is option 'A'. Can you explain this answer?
One of the angles of a triangle is 110 degree and the other two angles are equal what is the measure of each of these equal angles
a)
35 deg,35 deg
b)
40deg , 40deg
c)
11deg, 11 deg
d)
80deg , 80 deg
|
Dipanjan Goyal answered |
Let the two angles be x, y
x+y+110=180(angle sum property)
x+y=180-110
x+y=70
x=ytherefore x+x=70
2x =70
x=70/2
x=35,y=35
So x = y = 35
x+y+110=180(angle sum property)
x+y=180-110
x+y=70
x=ytherefore x+x=70
2x =70
x=70/2
x=35,y=35
So x = y = 35
Vertex opposite to the side RT of ΔRST is 
- a)T
- b)S
- c)R
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
Vertex opposite to the side RT of ΔRST is
a)
T
b)
S
c)
R
d)
None of these
|
Geetika Shah answered |
The vertex opposite to side RT is S.
Step-by-step explanation:
In the given question,
We have a triangle RST which has sides RS, ST and TR.
We know that a triangle consists three vertices and three sides each of which is particularly opposite to any one of the side of the triangle and vice-versa.
Therefore, we can see here that in the triangle RST.
The side RS is opposite to the vertex T.
The side ST is opposite to the vertex R.
and,
The side TR is opposite to the vertex S.
Hence, the correct answer will be S as side RT is opposite to S.
- a)50°
- b)60°
- c)55°
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
a)
50°
b)
60°
c)
55°
d)
None of these
|
Ishu answered |
Because it is an equilateral triangle
The value of x in the adjoining figure is
- a)15°
- b)90°
- c)30°
- d)45°
Correct answer is option 'D'. Can you explain this answer?
The value of x in the adjoining figure is
a)
15°
b)
90°
c)
30°
d)
45°
|
Shiksha Academy answered |
as two sides are equal so it is a isoceles triangle with one angle as 90° so other remaining two will be
each 45°
each 45°
A triangle in which all three sides are of equal lengths is called _________.
- a)Scalene
- b)Isosceles
- c)Equilateral
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
A triangle in which all three sides are of equal lengths is called _________.
a)
Scalene
b)
Isosceles
c)
Equilateral
d)
None of these
|
Kritika nair answered |
Equilateral Triangle
An equilateral triangle is a type of triangle in which all three sides are of equal lengths. It is a special case of a regular polygon, where all sides and angles are equal. In an equilateral triangle, all three angles are also equal to 60 degrees.
Characteristics of an Equilateral Triangle
- All three sides of an equilateral triangle are of equal length.
- All three angles of an equilateral triangle are equal to 60 degrees.
- The sum of the interior angles of an equilateral triangle is always 180 degrees.
- The altitude, median, and perpendicular bisectors of an equilateral triangle are concurrent.
- The circumcenter, incenter, and centroid of an equilateral triangle coincide and are the same point.
- The area of an equilateral triangle can be calculated using various formulas, such as A = (s^2 * √3) / 4, where s is the length of a side.
Visual Representation
To visualize an equilateral triangle, imagine a triangle with all three sides of equal length. Each angle of the triangle measures 60 degrees. It appears symmetrical and balanced.
Distinguishing from Other Types of Triangles
- Scalene Triangle: In a scalene triangle, all three sides have different lengths. Therefore, it is not an equilateral triangle.
- Isosceles Triangle: In an isosceles triangle, two sides have the same length, while the third side is of a different length. Since all three sides of an equilateral triangle are equal, it is not an isosceles triangle either.
Importance of Equilateral Triangles
- Equilateral triangles are commonly used in architecture and engineering because of their symmetry and stability.
- They are often found in the design of bridges, buildings, and other structures.
- The properties of equilateral triangles are used in various mathematical and geometrical calculations.
- They are also used in various puzzles and games.
Conclusion
An equilateral triangle is a special type of triangle in which all three sides are of equal lengths. It possesses unique properties and characteristics that distinguish it from other types of triangles. Equilateral triangles have practical applications in various fields and are important in mathematical and geometrical concepts.
An equilateral triangle is a type of triangle in which all three sides are of equal lengths. It is a special case of a regular polygon, where all sides and angles are equal. In an equilateral triangle, all three angles are also equal to 60 degrees.
Characteristics of an Equilateral Triangle
- All three sides of an equilateral triangle are of equal length.
- All three angles of an equilateral triangle are equal to 60 degrees.
- The sum of the interior angles of an equilateral triangle is always 180 degrees.
- The altitude, median, and perpendicular bisectors of an equilateral triangle are concurrent.
- The circumcenter, incenter, and centroid of an equilateral triangle coincide and are the same point.
- The area of an equilateral triangle can be calculated using various formulas, such as A = (s^2 * √3) / 4, where s is the length of a side.
Visual Representation
To visualize an equilateral triangle, imagine a triangle with all three sides of equal length. Each angle of the triangle measures 60 degrees. It appears symmetrical and balanced.
Distinguishing from Other Types of Triangles
- Scalene Triangle: In a scalene triangle, all three sides have different lengths. Therefore, it is not an equilateral triangle.
- Isosceles Triangle: In an isosceles triangle, two sides have the same length, while the third side is of a different length. Since all three sides of an equilateral triangle are equal, it is not an isosceles triangle either.
Importance of Equilateral Triangles
- Equilateral triangles are commonly used in architecture and engineering because of their symmetry and stability.
- They are often found in the design of bridges, buildings, and other structures.
- The properties of equilateral triangles are used in various mathematical and geometrical calculations.
- They are also used in various puzzles and games.
Conclusion
An equilateral triangle is a special type of triangle in which all three sides are of equal lengths. It possesses unique properties and characteristics that distinguish it from other types of triangles. Equilateral triangles have practical applications in various fields and are important in mathematical and geometrical concepts.
What is the measure of angles x?
- a)30°
- b)60°
- c)90°
- d)45°
Correct answer is option 'C'. Can you explain this answer?
What is the measure of angles x?
a)
30°
b)
60°
c)
90°
d)
45°
|
|
Anita Menon answered |
Since the two sides are equal, the angles opposite to them are also equal.
So x + 45° + 45° = 180° (Angles sum property)
x = 90°
Which is the longest side in the triangle PQR right angled at P?
- a)PQ
- b)QR
- c)PR
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
Which is the longest side in the triangle PQR right angled at P?
a)
PQ
b)
QR
c)
PR
d)
None of these
|
Dibyansu Paramanik answered |
QR because in a right angled triangle hypotenuse is the biggest line and here point P is 90 degrees so the QR line would make hypotenuse
The value of x in the adjoining figure is
- a)35°
- b)55°
- c)49°
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
The value of x in the adjoining figure is
a)
35°
b)
55°
c)
49°
d)
None of these
|
|
Tutorpedia Coaching answered |
y + 125 = 180
y = 55
and x+ y + 90 = 180
x + 55 + 90 = 180
x = 35
Find the value of unknown x in the adjoining figure.
- a)60°
- b)80°
- c)45°
- d)70°
Correct answer is option 'D'. Can you explain this answer?
Find the value of unknown x in the adjoining figure.
a)
60°
b)
80°
c)
45°
d)
70°
|
Rohan Pradhan Pradhan answered |
Correct answer is option d because:-
Total perimeter of the triangle is 180 degree
= x+50+60=180
50+60=110
110-180
=70 degree
So please this is explained answer please followed.
please
Total perimeter of the triangle is 180 degree
= x+50+60=180
50+60=110
110-180
=70 degree
So please this is explained answer please followed.
please
If the angles of a triangle are in the raitio 4:5:9. Find all the angles of a the triangle- a) 40 deg, 50 deg , 90 deg
- b)90 deg, 72 deg, 18 deg
- c)9 deg, 90 deg, 55 deg
- d)45 deg, 60 deg, 18 deg
Correct answer is option 'A'. Can you explain this answer?
If the angles of a triangle are in the raitio 4:5:9. Find all the angles of a the triangle
a)
40 deg, 50 deg , 90 deg
b)
90 deg, 72 deg, 18 deg
c)
9 deg, 90 deg, 55 deg
d)
45 deg, 60 deg, 18 deg
|
|
Dipanjan Goyal answered |
The sum of the angles of a triangle is 180 degrees. As the ratio of the angles of the triangle is 4:5:9 they can be taken to be 4x, 5x and 9x. 4x + 5x + 9x = 180
=> 18x = 180
=> x = 10
This gives the angles of the triangle as 40, 50 and 90 degrees.
Which type of triangle is formed by BC=7.2cm, AC=6 cm and ∠120o?
- a)An obtuse angled triangle.
- b)An acute angled triangle.
- c)A right angled triangle.
- d)An isosceles triangle.
Correct answer is option 'A'. Can you explain this answer?
Which type of triangle is formed by BC=7.2cm, AC=6 cm and ∠120o?
a)
An obtuse angled triangle.
b)
An acute angled triangle.
c)
A right angled triangle.
d)
An isosceles triangle.
|
Yashvi Singh answered |
Understanding the Triangle Inequality Theorem
The statement in the question refers to the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. This theorem is a fundamental concept in geometry and is applicable to all types of triangles, including equilateral, isosceles, and scalene triangles.
Explanation of the Triangle Inequality Theorem
To understand why the sum of the lengths of any two sides is greater than the length of the third side, we need to consider the possible scenarios that can occur when constructing a triangle.
Scenario 1: The sum of the lengths of two sides is equal to the length of the third side
In this scenario, when the sum of the lengths of two sides of a triangle is equal to the length of the third side, the three sides are said to be in a straight line, and the triangle is called a degenerate triangle. In such a case, the triangle collapses into a line segment, and it is not considered a valid triangle.
Scenario 2: The sum of the lengths of two sides is less than the length of the third side
In this scenario, when the sum of the lengths of two sides is less than the length of the third side, it is impossible to construct a triangle. When we try to connect the two shorter sides, they will not meet to form a closed figure.
Scenario 3: The sum of the lengths of two sides is greater than the length of the third side
In this scenario, when the sum of the lengths of two sides is greater than the length of the third side, it is possible to construct a triangle. When we try to connect the two shorter sides, they will meet to form a closed figure, and all three sides will be connected.
Conclusion
Based on the Triangle Inequality Theorem, we can conclude that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. This theorem is essential in determining whether a given set of side lengths can form a valid triangle or not. Therefore, option 'A' - greater than, is the correct answer.
The statement in the question refers to the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. This theorem is a fundamental concept in geometry and is applicable to all types of triangles, including equilateral, isosceles, and scalene triangles.
Explanation of the Triangle Inequality Theorem
To understand why the sum of the lengths of any two sides is greater than the length of the third side, we need to consider the possible scenarios that can occur when constructing a triangle.
Scenario 1: The sum of the lengths of two sides is equal to the length of the third side
In this scenario, when the sum of the lengths of two sides of a triangle is equal to the length of the third side, the three sides are said to be in a straight line, and the triangle is called a degenerate triangle. In such a case, the triangle collapses into a line segment, and it is not considered a valid triangle.
Scenario 2: The sum of the lengths of two sides is less than the length of the third side
In this scenario, when the sum of the lengths of two sides is less than the length of the third side, it is impossible to construct a triangle. When we try to connect the two shorter sides, they will not meet to form a closed figure.
Scenario 3: The sum of the lengths of two sides is greater than the length of the third side
In this scenario, when the sum of the lengths of two sides is greater than the length of the third side, it is possible to construct a triangle. When we try to connect the two shorter sides, they will meet to form a closed figure, and all three sides will be connected.
Conclusion
Based on the Triangle Inequality Theorem, we can conclude that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. This theorem is essential in determining whether a given set of side lengths can form a valid triangle or not. Therefore, option 'A' - greater than, is the correct answer.
ΔABC is right-angled at C. If AC = 5 cm and BC = 12 cm find the length of AB.
- a)17 cm
- b)13 cm
- c)7 cm
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
ΔABC is right-angled at C. If AC = 5 cm and BC = 12 cm find the length of AB.
a)
17 cm
b)
13 cm
c)
7 cm
d)
None of these
|
Varun Kapoor answered |
Acc to Pythagoras Theorem
AB2=AC2+BC2
AB2 = 52+122
=25+144 = 169
AB=13 cm
AB=13 cm
If one of the interior opposite angles of an exterior angle is 45∘ and the exterior angle is 130∘, what is the measure of the second interior opposite angle?- a)75∘
- b)85∘
- c)90∘
- d)95∘
Correct answer is option 'B'. Can you explain this answer?
If one of the interior opposite angles of an exterior angle is 45∘ and the exterior angle is 130∘, what is the measure of the second interior opposite angle?
a)
75∘
b)
85∘
c)
90∘
d)
95∘
|
Learning Enablers answered |
Using the exterior angle property:
Exterior Angle = Sum of Interior Opposite Angles
130∘= 45∘+ Other Angle
Other Angle = 130∘− 45∘= 85∘
Exterior Angle = Sum of Interior Opposite Angles
130∘= 45∘+ Other Angle
Other Angle = 130∘− 45∘= 85∘
The measure of three angles of a triangle are in the ratio 5:3:1.find the measure of this angles- a)100deg, 60deg, 20deg
- b)80deg, 30deg, 45deg
- c)120deg, 150deg, 30deg
- d)90deg, 90deg, 67deg
Correct answer is option 'A'. Can you explain this answer?
The measure of three angles of a triangle are in the ratio 5:3:1.find the measure of this angles
a)
100deg, 60deg, 20deg
b)
80deg, 30deg, 45deg
c)
120deg, 150deg, 30deg
d)
90deg, 90deg, 67deg
|
|
Dipanjan Goyal answered |
Let the angles be x
sum of the angles of a triangle=180
5x+3x+x=180
9x=180
x=20
angle 1=5x
=5*20=100
angle 2 =3x=3*20=60
angle 3=x=20
sum of the angles of a triangle=180
5x+3x+x=180
9x=180
x=20
angle 1=5x
=5*20=100
angle 2 =3x=3*20=60
angle 3=x=20
In the figure (not drawn to scale), ABCD is a square, ADE is an equilateral triangle and BFE is a straight line, find y. 
- a)90o
- b)45o
- c)75o
- d)15o
Correct answer is option 'C'. Can you explain this answer?
In the figure (not drawn to scale), ABCD is a square, ADE is an equilateral triangle and BFE is a straight line, find y.
a)
90o
b)
45o
c)
75o
d)
15o
|
Mrinalini Shah answered |
In ΔAEB,
∠A=∠DAE+∠BAD ⇒ ∠A=60o+90o=15o
And, AE=AB ⇒ ∠ABE=∠AEB
[Angles opposite to equal sides are equal]
Now, ∠A+∠ABE+∠AEB=180o (Angle sum property)
⇒ 2∠AEB=180o −150o = 30o ⇒ ∠AEB = 15o
Now, ∠E=60o ⇒ ∠DEF=60o−15o = 45o
∴ In ΔEFD, ∠DEF+∠EDF+∠EFD
= 180o ⇒ 45o+60o+y = 180o
⇒ y = 180o−(45o+60o) = 75o
∠A=∠DAE+∠BAD ⇒ ∠A=60o+90o=15o
And, AE=AB ⇒ ∠ABE=∠AEB
[Angles opposite to equal sides are equal]
Now, ∠A+∠ABE+∠AEB=180o (Angle sum property)
⇒ 2∠AEB=180o −150o = 30o ⇒ ∠AEB = 15o
Now, ∠E=60o ⇒ ∠DEF=60o−15o = 45o
∴ In ΔEFD, ∠DEF+∠EDF+∠EFD
= 180o ⇒ 45o+60o+y = 180o
⇒ y = 180o−(45o+60o) = 75o
Find angle x in
- a)60°
- b)160°
- c)80°
- d)100°
Correct answer is option 'A'. Can you explain this answer?
Find angle x in
a)
60°
b)
160°
c)
80°
d)
100°
|
Eduskill Classes answered |
Sum of interior opposite angles = Exterior angle
or 50° + x = 110°
or x = 60°
If the two legs of a right angled triangle are equal and the square of the hypotenuse is 100 sq units, what is the length of each leg?- a)10 units
- b)5√2 units
- c)10√2 units
- d)15 units
Correct answer is option 'B'. Can you explain this answer?
If the two legs of a right angled triangle are equal and the square of the hypotenuse is 100 sq units, what is the length of each leg?
a)
10 units
b)
5√2 units
c)
10√2 units
d)
15 units
|
|
Rainbow Rise Classes answered |
Let's solve the problem step by step:
Given:
- The two legs of a right-angled triangle are equal.
- The square of the hypotenuse is 100 square units.
Let the length of each leg be x units.
Using the Pythagorean theorem:
Find the measure of the angle x in the given figure.
- a)50o
- b)70o
- c)60o
- d)30o
Correct answer is option 'B'. Can you explain this answer?
Find the measure of the angle x in the given figure.
a)
50o
b)
70o
c)
60o
d)
30o
|
Gowri Dey answered |
∠EFD+∠FED = x
(Exterior angle property of a triangle)
⇒ 28o+42o = ∠x or ∠x = 70o
(Exterior angle property of a triangle)
⇒ 28o+42o = ∠x or ∠x = 70o
Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for chapter The Triangle and its Properties, Class 7, Mathematics . You can practice these practice quizzes as per your speed and improvise the topic. Q.How many medians a triangle can have?- a)1
- b)2
- c)3
- d)none of these
Correct answer is 'C'. Can you explain this answer?
Practice Quiz or MCQ (Multiple Choice Questions) with solutions are available for Practice, which would help you prepare for chapter The Triangle and its Properties, Class 7, Mathematics . You can practice these practice quizzes as per your speed and improvise the topic.
Q.
How many medians a triangle can have?
a)
1
b)
2
c)
3
d)
none of these
|
Anshu Basu answered |
In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid.
Find the measure of ∠LNM in the given figure.
- a)30o
- b)80o
- c)70o
- d)60o
Correct answer is option 'D'. Can you explain this answer?
Find the measure of ∠LNM in the given figure.
a)
30o
b)
80o
c)
70o
d)
60o
|
Kunal Mehra answered |
∠KLO = ∠MLN
∴ ∠MLN = 70o in ∠LMN
∴ ∠MLN = 70o in ∠LMN
Also,
∠MLN+∠LNM+∠LMN = 180o (Angle sum property)
⇒ 70o+∠LNM+50o=180o
⇒ ∠LNM = 180o−(70o+50o) = 60o
⇒ 70o+∠LNM+50o=180o
⇒ ∠LNM = 180o−(70o+50o) = 60o
In the given figure, the side QR of a △PQR has been produced to the point S. If ∠PRS = 115o and ∠P = 45o , then ∠Q is equal to,
- a)20o
- b)105o
- c)70o
- d)80o
Correct answer is option 'C'. Can you explain this answer?
In the given figure, the side QR of a △PQR has been produced to the point S. If ∠PRS = 115o and ∠P = 45o , then ∠Q is equal to,
a)
20o
b)
105o
c)
70o
d)
80o
|
|
Shiksha Academy answered |
∠PRS = ∠RPQ + ∠PQR (By exterior angle property)
⇒ 115º = 45º + ∠PQR
⇒ ∠PQR = 115º - 45º ⇒ ∠PQR = 70º
⇒ 115º = 45º + ∠PQR
⇒ ∠PQR = 115º - 45º ⇒ ∠PQR = 70º
Classify the following triangle on basis of their sides 
- a)(i)scalene, (ii) isoceles, (iii) equilateral
- b)(i) isosceles, (ii) right, (iii) equilateral
- c)(i) right, (ii) isosceles, (iii) equilateral
- d)(i) equilateral, (ii) scalene, (iii) isosceles
Correct answer is option 'A'. Can you explain this answer?
Classify the following triangle on basis of their sides
a)
(i)scalene, (ii) isoceles, (iii) equilateral
b)
(i) isosceles, (ii) right, (iii) equilateral
c)
(i) right, (ii) isosceles, (iii) equilateral
d)
(i) equilateral, (ii) scalene, (iii) isosceles
|
|
Rainbow Rise Classes answered |
(i) PQ = 5 cm, PR = 6 cm and QR = 7 cm
PQ ≠ PR ≠ QR
Thus, ∆PQR is a scalene triangle.
(ii) AB = 4 cm, AC = 4 cm, BC = 4.5 cm
AB = AC ≠ 4.5 cm
Thus, ∆ABC is an isosceles triangle.
(iii) MN = 3 cm, ML = 3 cm and NL = 3 cm
MN = ML = NL
Thus, ∆MNL is an equilateral triangle.
PQ ≠ PR ≠ QR
Thus, ∆PQR is a scalene triangle.
(ii) AB = 4 cm, AC = 4 cm, BC = 4.5 cm
AB = AC ≠ 4.5 cm
Thus, ∆ABC is an isosceles triangle.
(iii) MN = 3 cm, ML = 3 cm and NL = 3 cm
MN = ML = NL
Thus, ∆MNL is an equilateral triangle.
In the figure (not drawn to scale), ABC is an equilateral triangle and ABD is an isosceles triangle with DA = DB, find x.
- a)14o
- b)16o
- c)12o
- d)32o
Correct answer is option 'A'. Can you explain this answer?
In the figure (not drawn to scale), ABC is an equilateral triangle and ABD is an isosceles triangle with DA = DB, find x.
a)
14o
b)
16o
c)
12o
d)
32o
|
Anmol Iyer answered |
Since ABC is an equilateral triangle.
∴ ∠CAB =∠ABC =∠BCA = 60o
And ∠DBA = ∠DAB = (60o−x)
[∵ DA = DB]
In ΔDAB, ∠DBA+∠DAB+∠ADB =180o (Angle sum Property)
⇒ 2(60o−x)+88o = 180o
⇒ 2(60o−x) = 92o
⇒ 60o−x = 46o ⇒ x = 14o
∴ ∠CAB =∠ABC =∠BCA = 60o
And ∠DBA = ∠DAB = (60o−x)
[∵ DA = DB]
In ΔDAB, ∠DBA+∠DAB+∠ADB =180o (Angle sum Property)
⇒ 2(60o−x)+88o = 180o
⇒ 2(60o−x) = 92o
⇒ 60o−x = 46o ⇒ x = 14o
Find the measure of the angle ∠x in the given figure. 
- a)72o
- b)82o
- c)90o
- d)40o
Correct answer is option 'A'. Can you explain this answer?
Find the measure of the angle ∠x in the given figure.
a)
72o
b)
82o
c)
90o
d)
40o
|
|
Rainbow Rise Classes answered |
∠UXV = y (Vertically opposite angles)
∴ y = 45o
∴ y = 45o
In ΔXYZ, y+x+63o = 180o (Angle sum property)
⇒ 45o+x+63o = 180o
⇒ x = 180o−(45o+63o)
⇒ x= 180o−108o = 72o
⇒ 45o+x+63o = 180o
⇒ x = 180o−(45o+63o)
⇒ x= 180o−108o = 72o
If a triangle has angles measuring 40°, 60°, and x°, find the value of x.- a)70°
- b)80°
- c)90°
- d)100°
Correct answer is option 'B'. Can you explain this answer?
If a triangle has angles measuring 40°, 60°, and x°, find the value of x.
a)
70°
b)
80°
c)
90°
d)
100°
|
Kds Coaching answered |
The sum of all angles in a triangle is always 180°.
40° + 60° + x = 180°
x = 180° - (40° + 60°)
x = 180° - 100° = 80°
40° + 60° + x = 180°
x = 180° - (40° + 60°)
x = 180° - 100° = 80°
Find value of angle 1, 2, and 3, where angle y is equal to angle 3
- a)60 degrees
- b)70 degrees
- c)140 degrees
- d)20 degrees
Correct answer is option 'A'. Can you explain this answer?
Find value of angle 1, 2, and 3, where angle y is equal to angle 3
a)
60 degrees
b)
70 degrees
c)
140 degrees
d)
20 degrees
|
|
Kds Coaching answered |
Adding both sides, we have:
∠y + ∠1 + ∠2 = 3∠x
∠y + ∠1 + ∠2 = 3∠x
Therefore, 180° = 3∠x (Angle sum property of a triangle)
So,∠x = 180° ÷ 3 = 60°
∠x = 60°, ∠y = 60°
Therefore, the value of all angles is 60° and it is an equilateral triangle
Therefore, the value of all angles is 60° and it is an equilateral triangle
In a triangle, an exterior angle is always equal to __________.- a)The sum of the two adjacent interior angles
- b)The sum of the two opposite interior angles
- c)Twice the sum of all interior angles
- d)Half of the adjacent interior angles
Correct answer is option 'B'. Can you explain this answer?
In a triangle, an exterior angle is always equal to __________.
a)
The sum of the two adjacent interior angles
b)
The sum of the two opposite interior angles
c)
Twice the sum of all interior angles
d)
Half of the adjacent interior angles
|
|
Kds Coaching answered |
According to the exterior angle property, the measure of an exterior angle of a triangle is equal to the sum of the measures of its two interior opposite angles.
In ΔABC, AC = BC and ∠C = 110°. Find ∠A and ∠B.
- a)35°
- b)75°
- c)45°
- d)105°
Correct answer is option 'A'. Can you explain this answer?
In ΔABC, AC = BC and ∠C = 110°. Find ∠A and ∠B.
a)
35°
b)
75°
c)
45°
d)
105°
|
|
Shiksha Academy answered |
In given ΔABC, ∠C = 110°
Let ∠A = ∠B = x° (Angle opposite to equal sides of a triangle are equal)
x + x + 110° = 180° (Sum of all angles in a triangle is 180°)
⇒ 2x + 110° = 180°
⇒ 2x = 180° – 110°
⇒ 2x = 70°
⇒ x = 35°
Thus, ∠A = ∠B = 35°
Let ∠A = ∠B = x° (Angle opposite to equal sides of a triangle are equal)
x + x + 110° = 180° (Sum of all angles in a triangle is 180°)
⇒ 2x + 110° = 180°
⇒ 2x = 180° – 110°
⇒ 2x = 70°
⇒ x = 35°
Thus, ∠A = ∠B = 35°
Side opposite to the vertex Q of ΔPQR is
- a)PQ
- b)QR
- c)PR
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Side opposite to the vertex Q of ΔPQR is
a)
PQ
b)
QR
c)
PR
d)
None of these
|
|
Kds Coaching answered |
In Triangle ΔPQR, the side opposite to vertex Q is the side that does not touch vertex Q.
The side opposite to Q would be side PR, as it does not include the vertex Q.
for example,
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