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## Congruent and Similar Triangles

If you want to find similar triangles, use only SSS, SAS and AAA. Don't make an ASS of yourself.

# Identifying Congruent Triangles

In $$\triangle ABC$$ above, $$\angle A={66}^\circ,$$ $$M$$ is the midpoint of side $$\overline{BC},$$ and $$D$$ and $$E$$ are the feet of perpendicular drawn from $$M$$ to $$\overline{AB}$$ and $$\overline{AC},$$ respectively. If $$\lvert{\overline{MD}}\rvert=\lvert{\overline{ME}}\rvert,$$ what is the measure of $$\angle CME ?$$

Note: The above diagram is not drawn to scale.

Triangles $$ABC$$ and $$DEF$$ are congruent. If $$AB=3$$, $$BC=4$$ and $$CA=5$$, what is the length of $$DE$$?

In triangles $$ABC$$ and $$DEF$$, if we know that $$AB = EF, BC = DE$$ and $$\angle ABC = \angle DEF$$, are the triangles congruent?

In triangles $$ABC$$ and $$DEF$$, if we know that $$\angle ABC = \angle DFE$$, $$\angle BCA = \angle FED$$ and $$\angle CAB = \angle EDF$$, are the triangles congruent?

Triangles $$ABC$$ and $$DEF$$ are congruent. If $$AB = DE$$, $$BC = EF$$, $$\angle ABC = 37 ^ \circ$$ and $$\angle EDF = 39 ^ \circ$$, what is the measure (in degrees) of $$\angle EFD$$?

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