Question

congruence and triangles/sss and sas quiz
in the diagram, \\( \triangle a b c \cong \triangle q p r \\). complete the statement with the corresponding congruent part. (lesson 5.1)

1. \\( \angle r \cong \\) ?
2. \\( \overline{a b} \cong \\) ?
3. \\( \triangle b a c \cong \\) ?
4. \\( \triangle r p q \cong \\) ?
5. write a congruence statement for the congruent triangles shown at the right. (lesson 5.1)

decide whether enough information is given to show that the triangles are congruent. if so, tell which congruence postulate you would use. explain your reasoning. (lesson 5.2)
6.
7.
8.

Explanation:

1. $\angle R\cong\angle C$

Since $\triangle ABC\cong\triangle QPR$, corresponding angles are congruent. $\angle R$ in $\triangle QPR$ corresponds to $\angle C$ in $\triangle ABC$.

2. $\overline{AB}\cong\overline{QP}$

In congruent triangles $\triangle ABC\cong\triangle QPR$, $\overline{AB}$ in $\triangle ABC$ corresponds to $\overline{QP}$ in $\triangle QPR$.

3. $\triangle BAC\cong\triangle PQR$

By the congruence of $\triangle ABC\cong\triangle QPR$, when we re - label the vertices (since congruence is about the correspondence of all parts), $\triangle BAC$ (vertices $B$, $A$, $C$) corresponds to $\triangle PQR$ (vertices $P$, $Q$, $R$)

4. $\triangle RPQ\cong\triangle CAB$

Because $\triangle ABC\cong\triangle QPR$, reversing the order of vertices (while maintaining correspondence), $\triangle RPQ$ (vertices $R$, $P$, $Q$) corresponds to $\triangle CAB$ (vertices $C$, $A$, $B$)

5. $\triangle ZYX\cong\triangle FEG$

Looking at the side - side - side (SSS) markings (the tick marks on the sides), we can see that the sides of $\triangle ZYX$ correspond to the sides of $\triangle FEG$.

Answer:

1. $\angle C$
2. $\overline{QP}$
3. $\triangle PQR$
4. $\triangle CAB$
5. $\triangle ZYX\cong\triangle FEG$