UPSC CDS Math Triangles Questions

∠AMC = ∠BMD
Adding ∠CMD to both sides, we have
∴ ∠AMC + ∠CMD
=∠ BMD + ∠CMD
⇒ ∠AMD = ∠BMC
In ΔAMD and ΔBCM
∠DAM = ∠CBM (Given)
AM = BM (M is the mid-point of AB)
∠AMD = ∠BMC (Proved)
∴ ΔAMD ≅ Δ BCM (ASA congruence rule)