Question

Can someone write the answer in complete sentences please?

In the figure below, ∠ABC ≅ ∠DEC and ∠GFE ≅ ∠DCE. Point C is the point of intersection between segment AG and segment BD , while point E is the point of intersection between segment AG and segment DF.

picture is at the bottom

Prove ΔABC ∼ ΔGEF. (10 points)

Answer 1

Statements: Reason:

ΔABC is congruent to ΔDEF : Given

Angle ACB is congruent to angle ECG : Vertical angles

Angle CEG is congruent to angle DEF : Vertical angles

Angle DEF is congruent to angle ABC : Definition of congruent triangles

Angle CEG is congruent to angle ABC : Substitution property of equality

ΔABC is similar to Δ GEC : AA Similarity