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HELP
W NUMBER 3!!! PLSSS

HELP W NUMBER 3!!! PLSSS-example-1

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Answer:

∆HGF ≅ ∆ABC

Explanation:

You want to know which triangles in the given figure are congruent by SAS.

SAS

This congruence postulate says triangles are congruent if two corresponding sides and the angle between them are congruent. (Side-Angle-Side)

The triangles in the figure all have two corresponding sides marked. Only triangles HGF and ABC show angles G and B as congruent. Those angles are between the congruent sides and marked with a double arc.

Triangles HGF and ABC are congruent by SAS.

SSA

All of the triangles have an angle marked with a single arc next to the side marked with a double hash mark. There is no SSA congruence postulate, so the single-arc angle cannot be used with the marked sides to claim congruence of any of these triangles.

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Additional comment

When naming the congruent triangles, corresponding vertices need to be named in the same order. Here, the order we have chosen is to name the vertices on either end of the segment with the single hash mark, with the congruent angle vertex named second. That means the vertices of ∆ABC are named in alphabetical order. The vertices of ∆HGF are named in reverse-alphabetical order because of the way that triangle is marked.

A special case of SSA congruence is allowed for right triangles. In that case, it is called HL congruence. That works because it guarantees the longest side is opposite the congruent angles. In the general case, SSA offers no such guarantee.

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HELP W NUMBER 3!!! PLSSS-example-1
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