All questions of Practical Geometry for Class 8 Exam

Explanation:

A right-angled triangle is a triangle where one of its angles is a right angle, which means it is 90 degrees.

Maximum number of right angles in a right-angled triangle:

As per the definition of a right-angled triangle, it already has one right angle, which means the maximum number of right angles in a right-angled triangle can only be one.

Therefore, the correct answer is option 'B,' which states that the maximum number of right angles in a right-angled triangle is one.

Conclusion:

A right-angled triangle can only have one right angle, which is 90 degrees, and it is not possible to have more than one right angle in a triangle. Hence, option 'B' is the correct answer.

Explanation:

A right-angled triangle is a triangle that has one angle measuring 90 degrees. This angle is known as a right angle. The other two angles in a right-angled triangle are acute angles, meaning they are less than 90 degrees.

In a right-angled triangle, the sum of the other two angles must be equal to 90 degrees. Therefore, it is not possible for any angle in a right-angled triangle to be a right angle.

Maximum Number of Right Angles:

As mentioned above, a right-angled triangle has only one right angle. This is a fundamental property of a right-angled triangle and cannot be changed. Therefore, the correct answer is option 'B', which states that the maximum number of right angles in a right-angled triangle is 1.

Summary:

A right-angled triangle has one right angle, and the other two angles are acute angles. Therefore, the maximum number of right angles in a right-angled triangle is 1.

Let the breadth be 4x. So, length =5x we know perimeter is 2(l+b) which is equal to 72 or 2(5x+4x) or 18x=72 so x =4 sides are 16cm and 20 cm.

2

As the diagonals bisected each other i.e equal And the point of bisection is 90 degrees.

Square because square has every angle 90

Regular hexagon and exterior angles

A regular hexagon is a polygon with six sides and six equal angles. An exterior angle of a polygon is an angle formed by one side of the polygon and the extension of an adjacent side.

Formula for exterior angle of a regular polygon

In a regular polygon with n sides, each exterior angle measures 360/n degrees. Therefore, in a regular hexagon, each exterior angle measures:

360/6 = 60 degrees

Correct option

The question states that each exterior angle of the regular hexagon has a measure of 100 degrees. However, we know that the measure of each exterior angle of a regular hexagon is 60 degrees. Therefore, the correct answer is option C, which states that each exterior angle measures 100 degrees. This option is incorrect and does not match with the properties of a regular hexagon.

Therefore, the correct option is C.

All the sides of a regular polygon are equal in length.


A regular polygon is a polygon that has all sides of equal length and all angles of equal measure. In other words, it is a polygon that is both equilateral (all sides equal in length) and equiangular (all angles equal in measure).


A polygon is a closed figure formed by straight lines. Each line segment that forms the polygon is called a side. The sides of a polygon are connected at their endpoints, which are called vertices. The number of sides in a polygon determines its name. For example, a polygon with three sides is called a triangle, a polygon with four sides is called a quadrilateral, and so on.


A regular polygon has all sides and angles equal, while an irregular polygon has sides and/or angles of different lengths and measures.


Some examples of regular polygons include:
- Equilateral triangle: A triangle with all sides of equal length.
- Square: A quadrilateral with all sides of equal length and all angles of 90 degrees.
- Regular hexagon: A polygon with six sides of equal length and all angles of 120 degrees.


The fact that all sides of a regular polygon are equal in length can be proven using the properties of a regular polygon. Since a regular polygon is both equilateral and equiangular, we can show that all sides are equal by considering the angles and the length of the sides.

Let's consider a regular polygon with n sides. Each angle of the polygon measures (n-2) * 180 / n degrees. Since the polygon is equiangular, all these angles are equal.

Now, let's consider two consecutive sides of the polygon. The sum of the exterior angles of any polygon is always 360 degrees. In a regular polygon, each exterior angle measures 360 / n degrees. Since the polygon is equiangular, all exterior angles are equal.

From the properties of exterior angles, we know that the exterior angle and interior angle at a vertex are supplementary (add up to 180 degrees). Therefore, each interior angle of the regular polygon measures (n-2) * 180 / n degrees.

Using the fact that the interior angles are equal and sum up to 360 degrees, we can equate the two equations:
(n-2) * 180 / n = 360

Simplifying the equation, we get:
(n-2) * 180 = 360n

Expanding and rearranging, we get:
180n - 360 = 360n
180n - 360n = 360
-180n = 360
n = -2

Since the number of sides of a polygon cannot be negative, we have reached a contradiction. Therefore, the assumption that all sides of a regular polygon are not equal in length is false.

Therefore, it can be concluded that all sides of a regular polygon are equal in length. Thus, the correct answer is option B - equal in length.

3 sides and 2 angles there should be minimum 5 things in it to form a qaudrilateral. we cant form qaudrilateral by less then 5 main things. To form it we should know 5 things. For example - 2 sides and 3 included angles. or 3 sides and 2 included angles.

A

Because if we take any two points in the pentagon as given in option c) and join it, the line segment will completely remain inside the polygon.

Solution:

The sum of the measures of angles of a convex quadrilateral is 360°.

Explanation:

A convex quadrilateral is a four-sided polygon with all interior angles less than 180°. Since a polygon with n sides can be divided into n-2 triangles, the sum of the measures of angles of a polygon with n sides is (n-2) x 180°.

In the case of a convex quadrilateral, n=4. Therefore, the sum of the measures of angles of a convex quadrilateral is (4-2) x 180° = 2 x 180° = 360°.

Hence, the correct option is C.

The diagonals of a square bisect each other at a right angle.

Explanation:
- A square is a quadrilateral with all four sides equal in length and all four angles equal to 90 degrees.
- The diagonals of a square are the line segments that connect opposite corners of the square.
- When the diagonals of a square intersect, they divide each other into two equal halves.
- Since a square has four equal angles of 90 degrees, the diagonals of a square will also intersect at a right angle.

Proof:
- Let's consider a square ABCD with diagonals AC and BD.
- The diagonal AC divides the square into two right-angled triangles, namely triangle ABC and triangle CDA.
- Similarly, the diagonal BD divides the square into two right-angled triangles, namely triangle ABD and triangle BCD.
- In each of these triangles, the two legs are equal in length because the sides of the square are equal.
- By the property of a right-angled triangle, in a triangle where the two legs are equal, the angles opposite to the legs are also equal.
- Therefore, in triangle ABC and triangle CDA, angle BAC = angle CAD = 90 degrees/2 = 45 degrees.
- Similarly, in triangle ABD and triangle BCD, angle ABD = angle CBD = 90 degrees/2 = 45 degrees.
- Since angle BAC = angle CAD and angle ABD = angle CBD, the opposite angles of the intersecting diagonals AC and BD are equal.
- By the definition of a right angle, when two lines intersect and their opposite angles are equal, the lines are perpendicular to each other.
- Hence, the diagonals AC and BD of a square bisect each other at a right angle.

Therefore, the correct answer is option 'B' - right.

Because they have all diagonals in interior.

**Explanation:**

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. In a parallelogram, opposite angles are also equal.

To determine the type of parallelogram each of whose angles measures 90 degrees, we need to consider the properties of different quadrilaterals.

**1. Rectangle:** A rectangle is a parallelogram with all angles measuring 90 degrees. Therefore, a rectangle satisfies the condition stated in the question.

**2. Rhombus:** A rhombus is a parallelogram with all sides equal in length. While the opposite angles in a rhombus are equal, they are not necessarily 90 degrees. Therefore, a rhombus does not satisfy the condition stated in the question.

**3. Kite:** A kite is a quadrilateral with two pairs of adjacent sides that are equal in length. Kites do not have all angles measuring 90 degrees. Therefore, a kite does not satisfy the condition stated in the question.

**4. Trapezium:** A trapezium is a quadrilateral with one pair of parallel sides. Trapeziums do not have all angles measuring 90 degrees. Therefore, a trapezium does not satisfy the condition stated in the question.

Hence, the correct answer is **option A) rectangle**.

Triangle

120deegre

1

Construction of a Quadrilateral
The construction of a quadrilateral involves creating a figure with four sides and four angles. To uniquely construct a quadrilateral, certain information is required.

Diagonals and Sides
In the given scenario, if the two diagonals and three sides of a quadrilateral are known, the quadrilateral can be constructed uniquely. This is because the diagonals of a quadrilateral play a crucial role in determining its shape and size. By having the lengths of the two diagonals and three sides, the remaining side can be accurately determined using geometric principles such as the triangle inequality theorem and properties of quadrilaterals.

Uniqueness of Construction
When the diagonals and three sides of a quadrilateral are known, the construction becomes unique because the diagonals intersect at a specific point within the quadrilateral, dividing it into distinct triangles. The lengths of the sides and diagonals provide enough information to accurately position the vertices of the quadrilateral, ensuring that only one configuration is possible.
Therefore, by knowing the diagonals and three sides of a quadrilateral, a unique construction can be achieved based on the geometric properties and relationships within the figure.

Explanation:
A trapezoid is a quadrilateral with at least one pair of parallel sides. Let us analyze the given options one by one:

a) Only two opposite sides are parallel:
This property is true for all trapezoids. In a trapezoid, only two opposite sides are parallel, and the other two sides are non-parallel.

b) All angles are equal:
This property is not true for all trapezoids. In general, trapezoids do not have equal angles.

c) Consecutive angles are supplementary:
This property is also not true for all trapezoids. In general, the consecutive angles of a trapezoid are not supplementary.

d) The base angles are congruent:
This property is true only for isosceles trapezoids, which have two pairs of congruent angles. However, not all trapezoids are isosceles.

Therefore, the correct answer is option 'A': Only two opposite sides are parallel, which is true for all trapezoids.

Heptagon is a polygon of 7 sides

C

Explanation:

Convex and Concave Polygons:

Convex polygons are polygons in which all interior angles are less than 180 degrees, and all diagonals lie within the interior of the polygon. On the other hand, concave polygons have at least one interior angle greater than 180 degrees and have diagonals that extend outside the polygon.

Diagonals in Polygons:

Diagonals are line segments that connect two non-adjacent vertices in a polygon. In convex polygons, all diagonals remain within the interior of the polygon. However, in concave polygons, at least one diagonal extends outside the polygon's boundary.

Identification of Concave Polygons:

To determine if a polygon is concave, one must check if any of its interior angles are greater than 180 degrees. If such an angle exists, the polygon is concave. Concave polygons have portions of their diagonals outside their boundaries, making them different from convex polygons.

Answer:

The correct answer to the question is option 'D' - concave polygons. Concave polygons have portions of their diagonals extending outside their exterior boundaries, distinguishing them from convex polygons where all diagonals remain within the interior of the polygon.

Solution:
The sum of all angles of a quadrilateral is 360°. Therefore, the fourth angle can be found by subtracting the sum of the three given angles from 360°.

Given angles: 120°, 130°, 10°
Sum of given angles: 120° + 130° + 10° = 260°
Fourth angle = 360° - 260° = 100°

Therefore, the fourth angle of the quadrilateral is 100°.

Answer:
Option B

To construct a square, we only require the length of one side. The correct answer is option 'A'.

Explanation:
A square is a four-sided polygon with all sides of equal length and all angles equal to 90 degrees. The properties of a square make it unique and different from other polygons.

Constructing a square requires specific measurements and angles to ensure that all sides and angles are equal. However, only the length of one side is necessary to construct a square.

When we have the length of one side, we can use it to create the other sides of the square by measuring and marking the same length on each side. This will ensure that all sides are equal in length, which is a defining characteristic of a square.

Having the length of one side also allows us to determine the perimeter and area of the square. The perimeter is the sum of all four sides, which in the case of a square is four times the length of one side. The area is calculated by multiplying the length of one side by itself.

Therefore, knowing the length of one side is sufficient to construct a square and determine its properties such as side length, perimeter, and area.

The minimum possible interior angle in a regular polygon can be determined by using the formula for the interior angles of a polygon.

Formula for the interior angles of a polygon:
The sum of the interior angles of a polygon can be calculated using the formula:

Sum of interior angles = (n - 2) * 180 degrees

Where n represents the number of sides of the polygon.

Explanation:
In a regular polygon, all sides and angles are equal. Therefore, to find the measure of each interior angle, you divide the sum of the interior angles by the number of sides.

Let's consider a regular polygon with n sides. The formula for each interior angle can be written as:

Each interior angle = (Sum of interior angles) / n

To find the minimum possible interior angle, we need to find the smallest value for n that still forms a regular polygon. The smallest regular polygon is a triangle (n = 3).

Using the formula for the sum of interior angles, we can calculate the sum of angles for a triangle:

Sum of interior angles = (n - 2) * 180 degrees
= (3 - 2) * 180 degrees
= 1 * 180 degrees
= 180 degrees

Now, we can calculate the measure of each interior angle:

Each interior angle = Sum of interior angles / n
= 180 degrees / 3
= 60 degrees

Therefore, the minimum possible interior angle in a regular polygon is 60 degrees.

Equal

Explanation:

A parallelogram is a quadrilateral with opposite sides parallel to each other. It has several properties that distinguish it from other types of quadrilaterals. One of these properties is that its diagonals bisect each other.

In a parallelogram, the diagonals divide each other into two equal parts. This means that the two line segments that make up each diagonal are congruent. Therefore, the correct answer is option D, which states that the diagonals are congruent.

Why the Other Options are Incorrect:

Option A: If the diagonals bisect the angles to which they are drawn, it means that each diagonal divides one of the angles of the parallelogram into two equal parts. However, this property is not sufficient to prove that the parallelogram is a rectangle.

Option B: If the diagonals are perpendicular to each other, it means that the parallelogram is a rectangle, but this is not always the case. For example, a rhombus is a parallelogram with four equal sides, but its diagonals are perpendicular to each other without being a rectangle.

Option C: If the diagonals bisect each other, it means that they intersect at their midpoint. However, this property is not sufficient to prove that the parallelogram is a rectangle.

Conclusion:

In conclusion, a parallelogram must have diagonals that are congruent to be a rectangle. This property is one of the defining characteristics of a rectangle and is essential to its definition.

Yeha sure your answer is 4 sides and one diagonal take an example imagine a quadrilateral we can draw a quadrilateral only if it's 4 sides and one diagonal are given

Construction of a Parallelogram

To construct a parallelogram, we need to know two adjacent sides and one angle. Let's understand why this is the correct answer.

Parallelogram Properties:
1. Opposite sides of a parallelogram are parallel.
2. Opposite sides of a parallelogram are congruent (equal in length).
3. Opposite angles of a parallelogram are congruent.
4. Adjacent angles of a parallelogram are supplementary (add up to 180 degrees).
5. Diagonals of a parallelogram bisect each other.

Constructing a Parallelogram:
To construct a parallelogram, we start with two adjacent sides and one angle.

1. Draw the given two adjacent sides AB and AD using a ruler. Label the endpoints as A, B, C, and D.
2. From point A, construct an angle equal to the given angle. Label the vertex of this angle as E.
3. Using a compass, measure the length of one of the given sides and place the compass at point B. Draw an arc to intersect the angle bisector at F.
4. With the same compass setting, place the compass at point D and draw an arc to intersect the angle bisector at G.
5. Draw a line from point F to point D and extend it.
6. Draw a line from point G to point B and extend it.
7. The intersection of the extended lines from steps 5 and 6 will give us point C.
8. Connect points A, B, C, and D to complete the parallelogram ABCD.

Explanation:
By constructing a parallelogram using two adjacent sides and one angle, we ensure that the opposite sides are parallel and congruent. The given angle helps us determine the direction and shape of the parallelogram. The congruent opposite angles and supplementary adjacent angles are automatically satisfied due to the nature of parallelograms.

If we were given only the length of the parallel sides, we would not be able to determine the shape or the angles of the parallelogram. Similarly, if we were given only the measure of the angles, we would not have enough information to determine the length of the sides or the shape of the parallelogram.

Hence, the correct answer is option 'C' - Two adjacent sides and one angle.