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

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Important Properties of a Parallelogram
  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 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.