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

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1. Opposite sides are congruent

2. Opposite angels are congruent

3. Consecutive angles are supplementary

4. If one angle is right, then all angles are right.

5. The diagonals of a parallelogram bisect each other.

6. 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 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.

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