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
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Explanation:

Step1: Analyze triangle congruence for figure 7

• In \(\triangle QRP\) and \(\triangle UTS\), we have two sides equal (marked with ticks) but the included angles are not given as equal. So, we cannot prove them congruent by SAS.
• There is no information about all three sides (SSS) or other congruence criteria (like ASA, AAS). So, the triangles are not congruent.

Step2: Analyze triangle congruence for figure 8

• In \(\triangle ECD\) and \(\triangle ACB\), we have two sides equal (marked with ticks). Also, \(\angle ECD=\angle ACB\) (vertically - opposite angles).
• By the SAS (Side - Angle - Side) congruence criterion, \(\triangle ECD\cong\triangle ACB\).

Answer:

For figure 7: The triangles are not congruent.
For figure 8: \(\triangle ECD\cong\triangle ACB\) (by SAS).