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

1 thought on “35. Prove that a diagonal of a parallelogram divides it into two congruent triangles.​”

1. Step-by-step explanation:

   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

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