Question

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.

Prove ΔABC ∼ ΔGEF.

Answer 1

See Below.

Explanation:

We are given that:

`\angle ABC \cong \angle DEC\text{ and } \angle GFE \cong \angle DCE`

By vertical angles:

`\displaystyle \angle DEC\cong \angle GEF\text{ and } \angle DCE\cong \angle ACB`

Hence, by substitution:

`\displaystyle \angle ABC\cong \angle GEF\text{ and } \angle GFE\cong \angle ACB`

Then by Angle-Angle Similarity:

`\Delta ABC \sim \Delta GEF`