Question

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

Explanation:

Step1: Identify corresponding sides and angles

For the SAS (Side - Angle - Side) theorem, we need two sides and the included angle of one triangle to be equal to two sides and the included angle of another triangle.
In \(\triangle QRP\) and \(\triangle FEG\):

• Let's assume the side with three marks: In \(\triangle QRP\), one side has three marks and in \(\triangle FEG\) one side has three marks.
• The side with one mark: In \(\triangle QRP\), one side has one mark and in \(\triangle FEG\) one side has one mark.
• The included angle: The non - marked angle in \(\triangle QRP\) (the angle between the side with three marks and the side with one mark) and the non - marked angle in \(\triangle FEG\) (the angle between the side with three marks and the side with one mark) are equal.

Step2: Write the congruence statement

By the SAS theorem, \(\triangle QRP\cong\triangle FEG\)

Answer:

\(\triangle QRP\cong\triangle FEG\)