Question

The four triangles formed by joining the midpoints of the sides of a triangle respectively are:

• A. similar, not necessarily congruent
• B. congruent
• C. equilateral
• D. isosceles

Answer 1

Answer: (B)

In $△ABC$

$D$ is the midpoint of $BC$

$E$ is the midpoint of $BA$

$\therefore$ by midpoint theorem, $FO||AC$

$\frac{1}{2}AC=OF\Rightarrow OF=AE$

Similarly $OE=AB$ and $EF=BC$, using mid point theorem.

In $△AFE;△DEF;△EDC$

$AF=DE=FB=ED$, Proved

$FE=EF=BO=DC$, Proved

$AE=OF=FO=EC$ Proved

By SSS congruency.