We can see from the question three triangles, and we can see that we need to determine which two triangles are congruent by the SSS Theorem.
The side-side-side theorem indicates that if three sides of one triangle are congruent to the corresponding sides of the other triangle, then these two triangles are congruent by the SSS theorem.
To find it, we can proceed as follows:
1. We can see that the three triangles have the following marks on each side, and we can see that two of the three triangles, the one in the middle, and the one at the right have the same marks on their sides.
• Side RQ has two marks, and the side DF too.
• Side PQ has one mark, and the side DE too.
• Side PR has four marks, and the side EF too.
Notice that the first triangle (the one on the left) has one side with 3 marks. Therefore, the congruent triangles are the other two triangles.
2. Then to determine the corresponding sides of both triangles, we can use the drawing of them as follows:
3. Then, we can see that the corresponding sides are:
• PR ≅ EF
,
• PQ ≅ ED
,
• QR ≅ DF
Therefore, in summary, the two triangles that are congruent by the SSS are the triangles:
• Triangle PQR is congruent to EDF.
Or geometrically written:
• ΔPQR ≅ ΔEDF