Question

Given: PR is congruent to PQ and PT is congruent to PS. Prove: QS is congruent to RT. Write a paragraph proof.

a) Congruent triangles have equal angles.
b) By the transitive property, if PR is congruent to PQ and PT is congruent to PS, then PR is congruent to PS.
c) The corresponding sides of congruent triangles are congruent.
d) By the transitive property, if PR is congruent to PS and RS is congruent to RT, then PR is congruent to RT.

Answer 1

To prove that QS is congruent to RT, we can use the given information to show that angles and sides of the triangles are congruent.

Step-by-step explanation:

To prove that QS is congruent to RT, we need to use the given information that PR is congruent to PQ and PT is congruent to PS.

1. 
   
2. Using the fact that congruent triangles have equal angles, we can say that angle QPS is congruent to angle QPR and angle PSQ is congruent to angle PQR.
3. 
   
4. Using the transitive property, since PR is congruent to PQ and PT is congruent to PS, we can conclude that PR is congruent to PS.
5. 
   
6. By the corresponding sides of congruent triangles, we know that side QS is congruent to side PS and side RT is congruent to side PR.
7. 
   
8. Using the transitive property again, since PR is congruent to PS and RS is congruent to RT, we can conclude that PR is congruent to RT.

Combining steps 3 and 4, we can say that QS is congruent to RT.