Question

question 5(1 point)
justify the last two steps of the proof.
given: $overline{rs}congoverline{ut}$ and $overline{rt}congoverline{us}$
prove: $\triangle rstcong\triangle uts$
proof:

1. $overline{rs}congoverline{ut}$ 1. given
2. $overline{rt}congoverline{us}$ 2. given
3. $overline{st}congoverline{ts}$ 3. ?
4. $\triangle rstcong\triangle uts$ 4. ?

a reflexive property of $cong$; sas
b reflexive property of $cong$; sss
c symmetric property of $cong$; sss
d symmetric property of $cong$; sas

question 6(1 point)
state whether $\triangle abc$ and $\triangle aed$ are congruent. justify your answer.

a yes, by either sss or sas
b yes, by sss only
c yes, by sas only
d no; there is not enough information to conclude that the triangles are congruent.

question 7(1 point)
can you use the sas postulate, the aas theorem, or both to prove the triangles congruent?

a either sas or aas
b sas only
c aas only
d neither

question 8(1 point)
use the information given in the diagram. tell why $overline{mn}congoverline{pq}$ and $angle nomcongangle pmo$.

a transitive property, reflexive property
b given, reflexive property
c given, given
d reflexive property, transitive property

Explanation:

Question 5

The segment $\overline{ST}\cong\overline{TS}$ by the Reflexive Property (a segment is congruent to itself). Since we have $\overline{RS}\cong\overline{UT}$, $\overline{RT}\cong\overline{US}$ and $\overline{ST}\cong\overline{TS}$, we use the SSS (Side - Side - Side) congruence criterion to prove $\triangle RST\cong\triangle UTS$.

We are not given enough information about the side - lengths and angle - measures of $\triangle ABC$ and $\triangle AED$ to conclude they are congruent. There are no congruent side - length equalities or angle - equalities provided for SSS or SAS.

We have vertical angles which are equal. Also, we have two pairs of congruent sides. We can use the SAS (Side - Angle - Side) postulate as we have two sides and the included angle congruent. But we don't have two angles and a non - included side for AAS.

Answer:

b. Reflexive Property of $\cong$, SSS

Question 6