Q2 of 35 Page 67

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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