Question

in exercises 5 - 10, name the property that the statement illustrates. (see example 2.) 5. if $overline{pq}congoverline{st}$ and $overline{st}congoverline{uv}$, then $overline{pq}congoverline{uv}$. 6. $angle fcongangle f$ 7. if $angle gcongangle h$, then $angle hcongangle g$. 8. $overline{de}congoverline{de}$ 9. if $overline{xy}congoverline{uv}$, then $overline{uv}congoverline{xy}$. 10. if $angle lcongangle m$ and $angle mcongangle n$, then $angle lcongangle n$.

Explanation:

1. The statement "If $\overline{PQ}\cong\overline{ST}$ and $\overline{ST}\cong\overline{UV}$, then $\overline{PQ}\cong\overline{UV}$" illustrates the Transitive Property of Congruence as it shows that if one segment is congruent to a second and the second is congruent to a third, the first is congruent to the third.
2. The statement "$\angle F\cong\angle F$" illustrates the Reflexive Property of Congruence since an angle is always congruent to itself.
3. The statement "If $\angle G\cong\angle H$, then $\angle H\cong\angle G$" illustrates the Symmetric Property of Congruence as it shows that if one - angle is congruent to another, the second is congruent to the first.
4. The statement "$\overline{DE}\cong\overline{DE}$" illustrates the Reflexive Property of Congruence as a segment is congruent to itself.
5. The statement "If $\overline{XY}\cong\overline{UV}$, then $\overline{UV}\cong\overline{XY}$" illustrates the Symmetric Property of Congruence as it shows the reversibility of congruence for segments.
6. The statement "If $\angle L\cong\angle M$ and $\angle M\cong\angle N$, then $\angle L\cong\angle N$" illustrates the Transitive Property of Congruence as it shows the transitive relationship for angles.

Answer:

1. Transitive Property of Congruence
2. Reflexive Property of Congruence
3. Symmetric Property of Congruence
4. Reflexive Property of Congruence
5. Symmetric Property of Congruence
6. Transitive Property of Congruence