Question

In the following figure, ∠ACB = ∠AMN. Prove that ΔAMN ∼ ΔАСВ.

Answer 1

Given:

∠ACB = ∠AMN

Also, since B lies on AM and C lies on AN, the angle at A is common:

∠MAN = ∠CAB

Thus, in triangles △AMN and △ACB,

• ∠AMN = ∠ACB
• ∠MAN = ∠CAB

Therefore, by AA similarity,

△AMN ∼ △ACB

Hence proved.