Question

Given: DM⩭ME, BM⩭CM, D is the midpoint of AB, E is the midpoint of AC. Prove: ∠DBM⩭∠ECM

Answer 1

Complete Question

In Triangle ABC

Given: DM⩭ME, BM⩭CM, D is the midpoint of AB, E is the midpoint of AC.

Prove: ∠DBM⩭∠ECM

Answer:

Proved

Step-by-step explanation:

Given: DM⩭ME, BM⩭CM

Consider Triangles DBM and ECM in the diagram

$\dfrac{DM}{ME}= \dfrac{BM}{CM}$

Since DB and MC are the third lengths of the two triangles with two congruent lengths, then $DB \cong MC$

Therefore:

$\dfrac{MD}{ME}= \dfrac{BM}{CM}=\dfrac{DB}{MC}\\\\ \triangle DBM \cong \triangle ECM\\ By this fact:\\\angle DBM \cong \angle ECM$