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Answer:
See proof below
Step-by-step explanation:
Consider triangle with midpoints D, E, F of the sides BC, AC and AB, respectively. If D, E and F are midpoints of the sides BC, AC and AB, then
- EA=CE;
- DC=DB;
- FA=BF.
Triangle ABC is equilateral triangle, then
- m∠ABC=m∠ACB=m∠BAC=60°;
- AB=BC=AC.
If AB=BC=AC, then EA=CE=FA=BF=DC=DB.
By SAS theorem, ΔFAE≅ΔDCE≅ΔEBD.
Congruent triangles have congruent corresponding sides, then
EF=FD=DE. This means that triangle DEF is equilateral.
