Question

Two triangles ABC and DBC have common base BC. Suppose AB = DC and ∠ABC = ∠BCD. Prove that AC = BD.

Answer 1

Given: AB = DC and ∠ABC = ∠BCD

To Prove: AC = BD

Proof:

In ΔABC and ΔBDC:

BC = BC (Common)

∠ABC = ∠BCD (Given)

AB = DC (Given)

⇒ΔABC ≅ ΔBDC (SAS congruency)

⇒ BD = AC (Corresponding parts of congruent triangles)