Question

1. determine whether the par of triangles is congruent.

choose the correct answer below.
not congruent
congruent

1. (\triangle pqrcong\triangle mno). complete the congruence statement.

(overline{pr}cong?)
(overline{pr}cong)

1. (\triangle pqrcong\triangle mno). complete the congruence statement.

(angle pcong?)
(angle pcongangle)

1. would you use sss or sas to prove the triangles congruent? use only the marked sides/triangles and any shared sides. if there is not enough information to prove the triangles congruent by sss or sas, write

ot enough information\. explain your answer.
write a congruence statement and give a reason why the triangles are congruent. choose the correct answer below.
a. (\triangle sbccong\triangle kht), sas
b. (\triangle sbccong\triangle kht), sss
c. the two triangles are not necessarily congruent. there is not enough information.

Explanation:

Question 1: Determine whether the pair of triangles is congruent.

To determine if two triangles are congruent, we can use congruence criteria like SSS, SAS, ASA, AAS, or HL. Looking at the triangles (from the diagram, assuming corresponding sides and angles match), we check if corresponding parts are equal. If the triangles have corresponding sides equal (e.g., if the sides are marked or can be inferred to be equal) or angles, they are congruent. From the diagram (assuming standard congruence for such figures), the triangles are congruent.

When two triangles are congruent, their corresponding sides are congruent. In the congruence statement $\triangle PQR \cong \triangle NMD$, the order of the vertices matters. So, vertex $P$ corresponds to vertex $N$, vertex $Q$ corresponds to vertex $M$, and vertex $R$ corresponds to vertex $D$. Therefore, side $\overline{PR}$ (connecting $P$ and $R$) corresponds to side $\overline{ND}$ (connecting $N$ and $D$).

In a congruence statement of triangles, corresponding angles are congruent. For $\triangle PQR \cong \triangle MNO$, the order of the vertices gives the correspondence: $P$ corresponds to $M$, $Q$ corresponds to $N$, and $R$ corresponds to $O$. So, $\angle P$ (at vertex $P$) corresponds to $\angle M$ (at vertex $M$).

Answer:

Congruent

Question 2: $\triangle PQR \cong \triangle NMD$. Complete the congruence statement $\overline{PR} \cong \underline{\quad\quad}$