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
[tex]\dfrac{DM}{ME}= \dfrac{BM}{CM}\\[/tex]
Since DB and MC are the third lengths of the two triangles with two congruent lengths, then [tex]DB \cong MC[/tex]
Therefore:
[tex]\dfrac{MD}{ME}= \dfrac{BM}{CM}=\dfrac{DB}{MC}\\\\ \triangle DBM \cong \triangle ECM\\$By this fact:\\\angle DBM \cong \angle ECM[/tex]
