Question

Prove with reason that in Parallelogram-
(i)Each diagonal divides it into congruent triangles
(ii) the lengths of opposite sides are equal
(iii) the opposite angles are equal in magnitude​

Answer 1

Step-by-step explanation:

REF. Image.

consider Δ ABC and Δ ACD

Since the line segments AB+CD are parallel

to each other and AC is a transversal

∠ ACB = ∠ CAD.

AC = AC (common side)

∠CAB = ∠ ACD.

Thus, by ASA criteria

ΔABC ≅ ΔACD

The corresponding part of the congruent

triangle are congruent

AB = CD + AD = BC