ABCDEF Triangles

Geometry Level pending

A right-angled triangle $ABC$ has its right angle at $C$ . $D$ is the midpoint of $BC$ , $E$ is the midpoint of $AC$ , $F$ is the midpoint of $AB$ . Which of the following must be correct about triangle $DEF$ ?

DE is equal to (EF + FD)/2 One of its angle is 60 degrees. Its area is a quarter of the area of triangle ABC The length of angle bisector of DEF is equal to DF.

1 solution

A Former Brilliant Member
Jun 10, 2016

By the midpoint theorem, $DE//AB,EF//BC,DE//AC$ . Hence $\triangle DEF \sim \triangle ACB$ . By the midpoint theorem, $DE=0.5AB, EF= 0.5BC, DF=0.5AC$ . Thus, the area of triangle DEF is $\frac{1}{2}^2=\frac{1}{4}$ times the area of triangle ACB.

ABCDEF Triangles

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