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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