Question

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

Explanation:

Step1: Identify corresponding sides and angles

In \(\triangle QRP\), we have two sides and the included angle. In \(\triangle IGH\), we check for two sides and the included angle.
For \(\triangle QRP\): Let's assume the side - side - angle correspondence. The marked sides and the included angle.
For \(\triangle IGH\): The marked sides (one side is \(IG\), another is \(GH\)) and the included angle \(\angle G\) correspond to the sides and included angle of \(\triangle QRP\) (sides \(QR\) and \(RP\) with included angle \(\angle R\)).

Step2: Write the congruence statement

By the SAS (Side - Angle - Side) congruence theorem, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
We match the vertices: \(Q\) corresponds to \(I\), \(R\) corresponds to \(G\), \(P\) corresponds to \(H\)

Answer:

\(\triangle QRP\cong\triangle IGH\)