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