What Needs to Be Congruent to Show That ABC Is Congruent to PQR by SSS?

To show that two triangles are congruent by the SSS (side-side-side) theorem, all three corresponding sides must be shown to be of equal length. The letters SSS stand for the three sides of the two triangles.

For triangles ABC and PQR, it must be shown that AB=PQ, BC=QR and AC=PR. This is for a given correspondence ABC and PQR between the vertices of the two triangles.

Two triangles are said to be congruent if all three corresponding angles and the three corresponding sides are congruent. Two congruent triangles have identical size and shape.

There are various theorems by which two triangles can be shown to be congruent. These include the SAS (side-angle-side), RHS (right-hypotenuse-side) and ASA (angle-side-angle) theorems.