Question

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

Explanation:

Step1: Identify corresponding sides and angles

For triangle \( \triangle IJK\) and \( \triangle VUT\):

• In \( \triangle IJK\), we have a side - angle - side (SAS) configuration. The side with one mark, the included angle (marked angle at \(I\)), and the side with three marks.
• In \( \triangle VUT\), the side with three marks (corresponds to the side with three marks in \( \triangle IJK\)), the included angle (marked angle at \(U\) which is equal to the marked angle at \(I\) as per the congruence condition), and the side with one mark (corresponds to the side with one mark in \( \triangle IJK\)).

Step2: Write the congruence statement

When writing the congruence statement, we match the corresponding vertices. The vertex with the marked angle in \( \triangle IJK\) is \(I\), and in \( \triangle VUT\) is \(U\). The other vertices are matched based on the corresponding sides. So, \( \triangle IJK\cong\triangle VUT\)

Answer:

\(\triangle IJK\cong\triangle VUT\)