complete the proof that $\overline{ps} \cong \overline{rs}$.

| | statement | reason |
| --- | --- | --- |
| 1 | $\overline{qr} \cong \overline{pq}$ | given |
| 2 | $\overline{qs} \perp \overline{pr}$ | given |
| 3 | $\angle qpr \cong \angle prq$ | isosceles triangle theorem |
| 4 | $\angle ptq \cong \angle qtr$ | all right angles are congruent |
| 5 | $\triangle pqt \cong \triangle rqt$ | aas |
| 6 | $\angle pqs \cong \angle rqs$ | cpctc |
| 7 | $\overline{qs} \cong \overline{qs}$ | reflexive property of congruence |
| 8 | $\triangle pqs \cong \triangle rqs$ | sas |
| 9 | $\overline{ps} \cong \overline{rs}$ | |

Question

complete the proof that $\overline{ps} \cong \overline{rs}$.

| | statement | reason |
| --- | --- | --- |
| 1 | $\overline{qr} \cong \overline{pq}$ | given |
| 2 | $\overline{qs} \perp \overline{pr}$ | given |
| 3 | $\angle qpr \cong \angle prq$ | isosceles triangle theorem |
| 4 | $\angle ptq \cong \angle qtr$ | all right angles are congruent |
| 5 | $\triangle pqt \cong \triangle rqt$ | aas |
| 6 | $\angle pqs \cong \angle rqs$ | cpctc |
| 7 | $\overline{qs} \cong \overline{qs}$ | reflexive property of congruence |
| 8 | $\triangle pqs \cong \triangle rqs$ | sas |
| 9 | $\overline{ps} \cong \overline{rs}$ |  |

Accepted Answer

# Explanation:
## Step1: Recall CPCTC
CPCTC (Corresponding Parts of Congruent Triangles are Congruent) states that if two triangles are congruent, their corresponding parts (sides and angles) are congruent.
## Step2: Apply CPCTC to $	riangle PQS$ and $	riangle RQS$
We know from step 8 that $	riangle PQS \cong 	riangle RQS$ (by SAS). So, the corresponding sides $\overline{PS}$ and $\overline{RS}$ must be congruent by CPCTC.

# Answer:
CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

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QUESTION IMAGE

Question

Explanation:

Step1: Recall CPCTC

Step2: Apply CPCTC to $\triangle PQS$ and $\triangle RQS$

Answer:

	statement	reason
2	\\(\overline{qs} \perp \overline{pr}\\)	given
3	\\(\angle qpr \cong \angle prq\\)	isosceles triangle theorem
4	\\(\angle ptq \cong \angle qtr\\)	all right angles are congruent
5	\\(\triangle pqt \cong \triangle rqt\\)	aas
6	\\(\angle pqs \cong \angle rqs\\)	cpctc
7	\\(\overline{qs} \cong \overline{qs}\\)	reflexive property of congruence
8	\\(\triangle pqs \cong \triangle rqs\\)	sas
9	\\(\overline{ps} \cong \overline{rs}\\)