Theorem 8.1 : A diagonal of a parallelogram divides it into two congruent triangles Class 9

April 9, 2023April 9, 2023 by admin

Given: A parallelogram ABCD with AC as its diagonal.

To Prove: ΔABC ≅ ΔADC

Proof: In ΔABC and ΔCDA,

BC || AD and AC is a transversal.

So, ∠BCA = ∠DAC (Pair of alternate angles)

Also, AB || DC and AC is a transversal.

So, ∠BAC = ∠DCA (Pair of alternate angles)

and AC=CA (Common)

So, ΔABC ≅ ΔADC (ASA rule)

or, diagonal AC divides parallelogram ABCD into two congruent triangles ABC and CDA.