Question

using opposite angles test for parallelogram prove that every rectangle is a parallelogram​

Answer 1

Answer:

Step-by-step explanation:

Given:- A rectangle ABCD.

To prove:- ABCD is a parallelogram

Proof:-

Here in rect. ABCD, E is the mid points of diagonals.

∠ ECD = ∠EAB ( alternative angles)...(i)

∠ EAD =∠ECB (alternative interior angle)...(ii)

So, both the lines are parallel

Adding equation (i & ii)

∠EAD + ∠EAB  = ∠ECD + ∠ECB...(iii)

=) ∠DAB = ∠DCB

As, both the AB is parallel to DC and opposite angles are equal.

Thus, ABCD is a parallelogram

                                     (proved)