Final Answer:
In triangle MNO, with side lengths mn = 6, om = 9, and an unknown side no, and in triangle PQR, with corresponding side lengths pq = 6, rp = 9, and qr as no, the triangles are congruent by the Side-Side-Side (SSS) criterion. Therefore, side no corresponds to side qr, establishing the congruence between the two triangles.
3) pq
Step-by-step explanation:
Consider two triangles, MNO and PQR, where the lengths of their respective sides are provided as follows: mn = 6, om = 9, pq = 6, and rp = 9. The task is to determine the corresponding side to no and demonstrate the congruence of the triangles using the Side-Side-Side (SSS) criterion.
To begin, visualize triangle MNO with sides mn, om, and no. Mark mn as 6 units and om as 9 units. The length of side no remains unspecified initially. Concurrently, draw triangle PQR with sides pq, rp, and qr. Assign values of 6 units to pq and 9 units to rp, while qr is marked as no, mirroring the unknown side in triangle MNO.
In the context of SSS congruence, it becomes evident that side mn corresponds to side pq (both measuring 6 units), while side om corresponds to side rp (both measuring 9 units). The missing side no in triangle MNO corresponds to side qr in triangle PQR.
1. Draw a triangle MNO with sides mn, om, and no. Mark mn as 6 units, om as 9 units, but leave no as unknown for now.
2. Draw a triangle PQR with sides pq, rp, and qr. Mark pq as 6 units, rp as 9 units, and qr as no (since it corresponds to no in triangle MNO).
Now, you have two triangles:
```
M
/ \
/ \
/ \
N---------O
P
/ \
/ \
/ \
Q----------R
```
- Side mn corresponds to side pq (both marked as 6 units).
- Side om corresponds to side rp (both marked as 9 units).
- Side no corresponds to side qr (unknown in MNO, marked as no in PQR).
In conclusion, by the SSS criterion, triangles MNO and PQR are congruent. The congruence is established through the equality of corresponding side lengths: mn corresponds to pq, om corresponds to rp, and the previously undefined no corresponds to qr, thereby satisfying the conditions for congruence between the two triangles.