Question

in exercises 3 - 6, name the property that illustrates. (see example 2.) 3. if $overline{pq}congoverline{st}$ and $overline{st}congoverline{uv}$, then $overline{pq}congoverline{uv}$. 4. $angle fcongangle f$. 5. if $overline{xy}congoverline{uv}$, then $overline{uv}congoverline{xy}$. 6. if $angle lcongangle m$ and $angle mcongangle n$, then $angle lcongangle n$.

Explanation:

• For 3: Since $\overline{PQ}\cong\overline{ST}$ and $\overline{ST}\cong\overline{UV}$ implies $\overline{PQ}\cong\overline{UV}$, this is the transitive - property of congruence which states that if $a = b$ and $b = c$, then $a = c$ for congruent segments.
• For 4: $\angle F\cong\angle F$ shows the reflexive - property of congruence where any geometric figure is congruent to itself.
• For 5: If $\overline{XY}\cong\overline{UV}$, then $\overline{UV}\cong\overline{XY}$ demonstrates the symmetric - property of congruence which says that if $a = b$, then $b = a$ for congruent segments.
• For 6: Given $\angle L\cong\angle M$ and $\angle M\cong\angle N$ implies $\angle L\cong\angle N$, this is the transitive - property of congruence for angles.

Answer:

1. Transitive property of congruence.
2. Reflexive property of congruence.
3. Symmetric property of congruence.
4. Transitive property of congruence.