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

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Important properties of a parallelogram

Properties of a Parallellogram

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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:

Rectangle of ABCD

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.