NCERT Class 9 Solutions: Quadrilaterals (Chapter 8) Exercise 8.1 – Part 1

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:
Q2 If the diagonals of a parallelogram are equal, then show that it is a rectangle.
Solution:
Given,

To show ABCD is a rectangle we have to prove that one of its interior angle 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.