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Rufina [12.5K]
3 years ago
5

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.

Mathematics
1 answer:
I am Lyosha [343]3 years ago
8 0

Answer:

See Below.

Step-by-step 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

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