In the figure given below M is the midpoint of AB and DAB CBA and AMC BMD Then the triangle ADM is c...........

Quantitative Aptitude (CDS) Coordinate Geometry

In the figure given below, M is the midpoint of AB and $\small \angle$ DAB = $\small \angle$ CBA and $\small \angle$ AMC = $\small \angle$ BMD. Then the triangle ADM is congruent to the triangle BCM by

SAS rule

SSS rule

ASA rule

AAA rule

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Explanation:

∠AMC = ∠BMD ………(i)
∠CMD = ∠CMD (common angle)…….(ii)
Adding (i) and (ii), we get
∠AMC + ∠CMD = ∠BMD + ∠CMD
∠AMD = ∠BMC
∠DAM = ∠CBM
AM = BM
By, ASA
Triangle ADM ≅triangle BCM
Hence option (3)