Home
Class 14
MATHS
If the opposite sides of a quadrilateral...

If the opposite sides of a quadrilateral and also its diagonals are equal, then each of the angles of the quadrilateral is

A

`90^(@)`

B

`120^(@)`

C

`100^(@)`

D

`60^(@)`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the properties of a quadrilateral where both opposite sides and diagonals are equal. Let's break it down step by step. ### Step-by-Step Solution: 1. **Understanding the Properties**: - A quadrilateral has four sides. If opposite sides are equal, we can denote the sides as follows: let AB = CD and AD = BC. - Additionally, if the diagonals are equal, we denote them as AC = BD. 2. **Identifying the Quadrilateral Type**: - A quadrilateral with equal opposite sides and equal diagonals is a special type of quadrilateral. The properties suggest that it could be a rectangle or a rhombus. However, since both opposite sides and diagonals are equal, it specifically indicates that the quadrilateral is a rectangle. 3. **Properties of a Rectangle**: - In a rectangle, not only are the opposite sides equal, but all angles are right angles (90 degrees). This is a defining property of rectangles. 4. **Conclusion**: - Since we have established that the quadrilateral is a rectangle, we can conclude that each angle of the quadrilateral measures 90 degrees. ### Final Answer: Each of the angles of the quadrilateral is **90 degrees**.
Promotional Banner

Similar Questions

Explore conceptually related problems

Which of the following statements are true (T) and which are false (F)? In a parallelogram, the diagonals are equal. In a parallelogram, the diagonals bisect each other. In a parallelogram, the diagonals intersect each other at right angles. In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram. If all the angles of a quadrilateral are equal, it is a parallelogram. If three sides of a quadrilateral are equa, it is a parallelogram. If three angles of a quadrilateral are equal, it is a parallelogram. If all the sides of a quadrilateral are equal it is a parallelogram

If the opposite sides of a quadrilateral are equal, prove that the quadrilateral is a parallelogram.

If two opposite sides of a cyclic quadrilateral are equal,then the other two sides are parallel.

If two opposite sides of a cyclic quadrilateral are equal; then the other two sides are parallel.

Opposite angles two angles of a quadrilateral which are not adjacent angles are known as opposite angles of the quadrilateral.

Given statements . Identify the statements given below as contrapositive or converse of each other. If a quadrilateral is a parallelogram, then its diagonals bisect each other. (i) If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram. (ii) If the diagronals of a quadrilateral bisect each other, then it is a parallelogram.

A quadrilateral whose all sides, diagonals and angles are equal is a

If the diagonals of a quadrilateral are equal and bisect each other, then the quadrilateral is a