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Home / Geometry / Prove that a diagonal of a parallelogram divides it into two congruent triangles.

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

General enunciation: We have to prove that a diagonal of a parallelogram divides it into two congruent triangles.

Particular enunciation: Let the diagonal of the parallelogram ABCD is BD. The diagonal BD divides the parallelogram into two triangles ABD and BCD.

We have to prove that ∆ABD ≅ ∆BCD

## Proof: Since ABCD is a parallelogram and the opposite sides and angles of a parallelogram are equal.

∴ AB = CD, BC = AD

In ∆ABD and ∆BCD

AB = CD, BC = AD

and included ∠ABC = included ∠ADC

∴ ∆ABD ≅ ∆BCD.       [ side-angle-side]                                     (Proved)

## If two triangles have the three sides of the one equal to the three sides of the other, each to each, then they are equal in all respects.

If two triangles have the three sides of the one equal to the three sides ...