Question

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

Select Congruent or Not Congruent for each pair of triangles.

△ABC and △MNP
△ABC and △EFG
△ABC and △STU
△EFG and △MNP
△EFG and △STU
△STU and △MNP

Answer 1

Not Congruent: ABC and MNP , ABC and EFG , EFG and STU , STU and MNP.

Congruent: ABC and STU , EFG and MNP.

Explanation:

Answer 2

Not congruent; not congruent; congruent; congruent; not congruent; not congruent.

Explanation:

The base of △ABC, BC, is 2 units. The height of △ABC, extending from A to BC, is 3 units. This means that any triangle congruent to this will have a base of 2 and a height of 3.

△MNP has a base of 2; however, its height (from M to NP) is 4 units. Therefore they are not congruent.

△EFG has a base of 2 and a height of 4; it and △ABC are not congruent.

△STU has a base of 2 and a height of 3; it is congruent to △ABC.

△EFG has a base of 2 and a height of 4, just as △MNP; they are congruent.

Since △STU is congruent to △ABC, and we know that △EFG is not congruent to △ABC, we know that △EFG is not congruent to △STU.

Since △MNP is congruent to △EFG, and △EFG is not congruent to △STU, then △MNP is not congruent to △STU.