Question

directions: state whether the triangles can be proven congruent, if possible, by sss or sas. include a congruency statement for all congruent triangles.
triangle congruency: sss vs. sas

1. sas; \\( \triangle qyt \cong \triangle cmp \\)
2. sss; \\( \triangle adc \cong \triangle cba \\)

3.
4.
5.
6.
7.

1. sas; \\( \triangle ecd \cong \triangle acb \\)

Explanation:

Step1: Analyze figure 1

Check if two sides and included angle (SAS) or three sides (SSS) are equal. In figure 1, we have SAS: $\triangle QYT\cong\triangle CMP$.

Step2: Analyze figure 2

Check for SSS or SAS. Here, SSS: $\triangle BDC\cong\triangle CBA$.

Step3: Analyze figure 3

Check for congruence criteria. There is no SSS or SAS, so no congruence.

Step4: Analyze figure 4

Check for congruence criteria. There is no SSS or SAS, so no congruence.

Step5: Analyze figure 5

Check for congruence criteria. There is no SSS or SAS, so no congruence.

Step6: Analyze figure 6

Check for congruence criteria. There is no SSS or SAS, so no congruence.

Step7: Analyze figure 7

Check for congruence criteria. There is no SSS or SAS, so no congruence.

Step8: Analyze figure 8

Check for SAS. We have $\triangle ECD\cong\triangle ACB$ by SAS.

Answer:

1. $\triangle QYT\cong\triangle CMP$ (SAS)
2. $\triangle BDC\cong\triangle CBA$ (SSS)
3. No congruence
4. No congruence
5. No congruence
6. No congruence
7. No congruence
8. $\triangle ECD\cong\triangle ACB$ (SAS)