Question

which two triangles are congruent by the sas theorem? complete the congruence statement.

Explanation:

Step1: Identify corresponding sides and angles

For triangle \( \triangle RQS\) and \( \triangle HGI\):

• In \( \triangle RQS\), we have two sides and the included angle. Let's assume the side - side - angle correspondence.
• In \( \triangle HGI\), we check the side - side - angle correspondence.

We know that for the SAS (Side - Angle - Side) congruence criterion, two sides and the included angle of one triangle must be equal to two sides and the included angle of another triangle.
In \( \triangle RQS\) and \( \triangle HGI\):
Let's assume the sides:
If we consider the side with one mark, the side with two marks and the included angle (the non - marked angle between them).
We can see that:

• One side (with one mark) of \( \triangle RQS\) is equal to one side (with one mark) of \( \triangle HGI\)
• One side (with two marks) of \( \triangle RQS\) is equal to one side (with two marks) of \( \triangle HGI\)
• The included angles (the angles that are not marked with the side - length marks) are equal.

Answer:

\(\triangle RQS\cong\triangle HGI\)