Question

Which pairs of triangles can be shown to be congruent using rigid motions?



Select Congruent or Not congruent for each pair of triangles.

Congruent Not congruent
△ABC and △MPN


△ABC and △EGF


△ABC and △STU


△EFG and △MNP


An x y coordinate plane is shown. In quadrant 1 triangle A B C has vertices at begin ordered pair 2 comma 3 end ordered pair, begin ordered pair 6 comma 4 end ordered pair and begin ordered pair 2 comma 5 end ordered pair, respectively. In quadrant 2 triangle E F G has vertices at begin ordered pair negative 5 comma 2 end ordered pair, begin ordered pair negative 3 comma 2 end ordered pair and begin ordered pair negative 4 comma 5 end ordered pair, respectively. In quadrant 3 triangle S T U has vertices at begin ordered pair negative 2 comma negative 3 end ordered pair, begin ordered pair negative 6 comma negative 4 end ordered pair and begin ordered pair negative 2 comma negative 5 end ordered pair, respectively. In quadrant 4 triangle M N P has vertices at begin ordered pair 5 comma negative 2 end ordered pair, begin ordered pair 3 comma negative 2 end ordered pair and begin ordered pair 4 comma negative 5 end ordered pair, respectively.

Answer 1

Answers with brief reasons:

- △ABC and △MPN — Not congruent.
ABC has side lengths √17, 2, √17; MPN has √10, 2, √10 (different lengths).

- △ABC and △EGF — Not congruent.
EGF has side lengths √10, 2, √10 while ABC is √17, 2, √17 (different).

- △ABC and △STU — Congruent.
STU has the same side lengths √17, 2, √17, and a 180° rotation about the origin sends A→S, B→T, C→U.

- △EFG and △MNP — Congruent.
Both have side lengths √10, 2, √10, and a 180° rotation about the origin sends E→M, F→N, G→P.