Question

60 POINTS PLEASE HELP AND ANSWER THIS WITH THE SHOWN WORK

Answer 1

m∠DBF = 92°

Explanation:

Use the Triangle Midsegment Theorem to solve this problem:

The segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side.

Therefore, according to this theorem:

AE = EC, therefore E is the midpoint of AC.

BF = FC, therefore F is the midpoint of BC.

Therefore AB is parallel to EF.

ΔECF is similar to ΔACB. Therefore, if m∠EFC = 92°, then m∠DBF = 92°

Answer 2

∠ DBF = 92°

Explanation:

A segment joining the midpoints of a triangle is

• Parallel to the third side

Given AE = EC , then C is the midpoint of side AC

Given BF = BC , then F is the midpoint of BC

Then EF is a midline segment

Therefore EF is parallel to the third side AB

∠ EFC and ∠ DBF are corresponding angles and are congruent ( equal), so

∠ DBF = ∠ EFC = 92°