# NCERT Class 9 Solutions: Quadrilaterals (Chapter 8) Exercise 8.1 – Part 1 (For CBSE, ICSE, IAS, NET, NRA 2022)

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- Opposite sides are congruent
- Opposite angels are congruent
- Consecutive angles are supplementary
- If one angle is right, then all angles are right.
- The diagonals of a parallelogram bisect each other.
- Each diagonal of a parallelogram separates it into two congruent triangles.

Q 1. The angles of quadrilateral are in the ratio . Find all the angles of the quadrilateral.

Solution:

Suppose the measures of four angles are .

Sum of the interior angles of the quadrilateral

Now,

Therefore, Angles of the quadrilateral are:

Q-2 If the diagonals of a parallelogram are equal, then show that it is a rectangle.

Solution:

Given,

To show ABCD is a rectangle we must prove that one of its interior angles is right angled.

Proof,

In and , (Common) (Opposite sides of a parallelogram are equal) (Given)

Therefore, by SSS congruence condition. (by Corresponding Parts of Congruent Triangles)

also, (Sum of the angles on the same side of the transversal)

Thus, ABCD is a rectangle.