Question

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

Explanation:

Step1: Identify corresponding sides

In $\triangle HGI$, side $HG$ has three marks, $GI$ has two marks, and $HI$ has one mark. In $\triangle RQS$, side $RQ$ has one mark, $QS$ has two marks, and $RS$ has three marks. In $\triangle YXW$, side $YX$ has one mark, $XW$ has three marks, and $YW$ has two marks.

Step2: Match triangles by SSS

By SSS (Side - Side - Side) congruence theorem, we match the triangles with equal - marked sides. $\triangle HGI$ and $\triangle YXW$ have sides with the same number of marks. $HG = XW$ (three marks), $GI=YW$ (two marks), $HI = YX$ (one mark).

Answer:

$\triangle HGI\cong\triangle YXW$