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Can you apply all of the properties you learned in this lesson?

This lesson introduced you to a total of four properties of congruent triangles--CPCTC, SSS, SAS, and ASA. Practice applying these properties to determine congruence. In your notebook, answer each question, then click the Answer button to check your work.

CPCTC Question 1

Congruent triangles.

Triangles ABC and EFG are congruent. Write the corresponding congruent angles for these two triangles.

\(\mathsf{ \angle }\)A ≅ \(\mathsf{ \angle }\)E
\(\mathsf{ \angle }\)B ≅ \(\mathsf{ \angle }\)F
\(\mathsf{ \angle }\)C ≅ \(\mathsf{ \angle }\)G

CPCTC Question 2

Congruent triangles.

Triangles ABC and EFG are congruent. Write the congruent corresponding sides of these two triangles.

\(\small\mathsf{ \overline{AB} }\) ≅ \(\small\mathsf{ \overline{EF} }\)
\(\small\mathsf{ \overline{BC} }\) ≅ \(\small\mathsf{ \overline{FG} }\)
\(\small\mathsf{ \overline{AC} }\) ≅ \(\small\mathsf{ \overline{EG} }\)

Triangle Congruence Question 1

Two congruent triangles labeled with two angles and a side.

Is there enough information to determine if these two triangles are congruent? If yes, are they congruent by SAS, ASA, or SSS?

These two triangles are congruent by ASA.

Triangle Congruence Question 2

Two congruent triangles labeled with an angle and a side.

Is there enough information to determine if these two triangles are congruent? If yes, are they congruent by SAS, ASA, or SSS?

We only know information about one pair of angles and one pair of sides. Therefore, there is not enough information to determine if these two triangles are congruent.