In isosceles triangle ∆abc, bm is the median to the base ac . point d is on bm . prove the following triangle congruencies: ∆amd ≅ ∆cmd.

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Step-by-step explanation:

In isosceles triangle ∆ABC, BM is the median to the base AC.

Since ΔABC is isosceles, then AB ≅ BC.

Since BM is the median, then AM ≅ MC.

Consider triangles ABM and CBM. In these triangles,

So, ΔABM ≅ ΔCBM by SSS postulate. Congruent triangles have conguent corresponding sides and angles, so

∠AMB ≅ ∠CMB.

Consider triangles AMD and CMD. In these triangles,

so ΔAMD ≅ ΔCMD by SAS postulate

step-by-step explanation: