Congruence of triangle

Question

If AB=DC=4 cm, <ABC=<DCB=130° and <D =20°.  AC and DB intersect  at point M. Prove that ABM is congruent to DCM

Answer 1

AB = DC = 4             Given

∠C = ∠B = 130°         Given

∠D = 20°                  Given

∠AMB = ∠CMB           Vertical angles

∠A = 20º                  Sum of interior angles of triangle = 180°

∠A ≅ ∠D                   Substitution, Equality Property of Congruence

 

Δ ABM ≅ ΔDCM         ASA Congruence (∠A ≅ ∠D, AB ≅ CD, ∠B ≅ ∠D)