Q. 23.9( 31 Votes )
Using opposite angles test for parallelogram, prove that every rectangle is a parallelogram.
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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