Question

date: 14/10/25 bell: homework 5: proving triangles congruent sss & sas this is a 2 - page document! state whether the triangles could be proven congruent, if possible, by sss or sas. then, write a congruency statement. #1 is done for you! 1. sss \\( \triangle wmc\cong\triangle ypf \\) 2. 3. 4. 5. 6. complete the proofs below using the most appropriate method, sss or sas. 7. given: \\( \overline{am}\cong\overline{cp},\overline{cm}\cong\overline{gp} \\), c is the midpoint of \\( \overline{ag} \\) prove: \\( \triangle acm\cong\triangle cgp \\) 8. given: \\( \overline{pq}\cong\overline{rs},\angle pqr\cong\angle srq \\) prove: \\( \triangle pqr\cong\triangle srq \\)

Explanation:

7.

Step1: Use the mid - point property

Since \(C\) is the mid - point of \(\overline{AG}\), by the definition of a mid - point, \(\overline{AC}\cong\overline{CG}\).

Step2: Apply the SSS congruence criterion

We have \(\overline{AM}\cong\overline{CP}\) (given), \(\overline{CM}\cong\overline{GP}\) (given), and \(\overline{AC}\cong\overline{CG}\) (from step 1). By the Side - Side - Side (SSS) congruence criterion, \(\triangle ACM\cong\triangle CGP\).

8.

Step1: Identify the common side

\(\overline{QR}\cong\overline{RQ}\) (reflexive property of congruence, a segment is congruent to itself).

Step2: Apply the SAS congruence criterion

We have \(\overline{PQ}\cong\overline{RS}\) (given), \(\angle PQR\cong\angle SRQ\) (given), and \(\overline{QR}\cong\overline{RQ}\) (from step 1). By the Side - Angle - Side (SAS) congruence criterion, \(\triangle PQR\cong\triangle SRQ\).

Answer:

7.

Statements	Reasons
2. \(\overline{CM}\cong\overline{GP}\)	2. Given
3. \(C\) is the mid - point of \(\overline{AG}\)	3. Given
4. \(\overline{AC}\cong\overline{CG}\)	4. Definition of mid - point
5. \(\triangle ACM\cong\triangle CGP\)	5. SSS

8.

Statements	Reasons
2. \(\angle PQR\cong\angle SRQ\)	2. Given
3. \(\overline{QR}\cong\overline{RQ}\)	3. Reflexive property of congruence
4. \(\triangle PQR\cong\triangle SRQ\)	4. SAS