Question

A diagonal of a parallelogram divides it into two congurent triangles​

Answer 1

Given: Parallelogram ABCD

Prove: AB≅DCAnd AD≅BC

Parallelogram ABCD[Given]

AB ∥ DCand AD ∥ BC.

[Definition of a parallelogram]

∠BAC≅∠DCA

∠ABD≅∠BDC

∠DAC≅∠BCA

∠ADB≅∠DBC.

[Alternate interior angles are congruent if lines are parallel]

BD≅BD

AC≅AC. [Reflexive Property]

ΔADB≅ΔCBD

ΔADC≅ΔCBA

By ASA rule

AB≅DCand AD≅BC

CPCTC

❤HENCE PROVED ✔️