Q. 23.9( 31 Votes )

Using opposite angles test for parallelogram, prove that every rectangle is a parallelogram.

Answer :

Opposite angle property of parallelogram says that the opposite angles of a parallelogram are congruent.

Given a rectangle which had at least one angle as 90°.



If A is 90° and AD = BC (opposite sides of rectangle are and =)


AB is transversal


A + B = 180 (angles on the same side of transversal is 180°)


But B + C is 180 (AD BC, opposite sides of rectangle)


A = C = 90°


Since opposite s are equal this rectangle is a parallelogram too.


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