Question

Prove that a diagonal of a parallelogram divide it into two congruent triangles.​

Answer 1

Answer:

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In

BAC and

DCA

1 =

2

3 =

4 [alternate pair]

AC = AC (common)

Therefore, diagonal of a parallelogram divides it into two congruent triangles.

Answer 2

In ΔABC and ΔACD

AB || CD and AC is a transversal

Thus,

∠ ACB = ∠ CAD.

AC = AC (common side)

∠CAB = ∠ ACD.

Thus, by ASA congruency ΔABC ≅ ΔACD

The corresponding part of the congruent triangle are congruent

Therefore,

AB = CD + AD = BC

Hence proved