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NCERT Class 9 Solutions: Quadrilaterals (Chapter 8) Exercise 8.1 β 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:
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.