Question

decide whether enough information is given to prove that \\( \triangle efh \\) and \\( \triangle ghf \\) are congruent using the sas congruence theorem. explain
options:

• yes, two pairs of sides and the included angles are congruent.
• yes, two pairs of sides and a pair of angles not included by the sides are congruent.
• no, one of the congruent angles is not the included angle.
• no, there is only one pair of congruent sides

Explanation:

Step1: Analyze the given information

From the diagram, we can see that \(FH = FH\) (common side). Also, \(EF = GH\) and \(EH = GF\) (marked as equal). And the included angle \(\angle EFH=\angle GHF\) (given).

Step2: Check the SAS (Side - Angle - Side) congruence condition

The SAS congruence theorem states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.
Here, in \(\triangle EFH\) and \(\triangle GHF\), we have two pairs of sides (\(EF = GH\), \(FH = FH\)) and the included angle (\(\angle EFH=\angle GHF\)) congruent.

Answer:

yes, Two pairs of sides and the included angles are congruent.