Coupon Accepted Successfully!


Theorem 1 - The Diagonal Divides a Parallelogram into Two Congruent Triangles.

Given: A parallelogram ABCD.
To Prove: ΔABD Δ DCB

Construction: Join BD

Proof :
Since ABCD is a parallelogram. AB||CD and BD is the transversal.
In Δ ABD and Δ DCB,

ABD = CDB (Alternate interior angles)
Since AD||BC

ADB = CBD ……(Alternate interior angles)
AB = CD (opposite sides of a parallelogram)
AD = CB (opposite sides of a parallelogram)
BD = DB (common)

Diagonal BD divides parallelogram ABCD into two congruent triangles ABD and DCB
Similarly diagonal AC divides ||gmABCD into two congruent triangles ABC and ADC.
Hence the diagonal divides a parallelogram into two congruent triangles.

Test Your Skills Now!
Take a Quiz now
Reviewer Name