Question

D,E and F are respectively the mid points of sides BC ,CA and AB of an equilateral triangle . △ABC. Prove that △DEF is also an equilateral triangle

Answer 1

See proof below

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.