Triangle Congruence: ASA and AAS — Quiz

Question 14 • Geometry

Which of these triangle pairs can be mapped to each other using a translation and a rotation about point A?

Answer

Image with description Triangles Q R A and K P L are shown. Triangle Q R A is reflected and then shifted to the right to form triangle K P L.. Angle Q A R is congruent to angle K L P, side R A is congruent to P L, and angle Q R A is congruent to angle K P L.

Image with description Triangles Q R A and K P L are shown. Triangle Q R A is rotated about point A and then is shifted down and to the left to form triangle K P L. Angle Q A R is congruent to angle K L P, side R A is congruent to P L, and angle Q R A is congruent to angle K P L.

Image with description Triangles Q R A and K P A are connected at point A. Triangle K P A is rotated to form triangle Q R A. Angle Q A R is congruent to angle K A P, side R A is congruent to A P, and angle Q R A is congruent to angle K P A.

Explanation

Choice B describes rotating triangle QRA about point A and then translating it down and to the left. A rotation and a translation preserve the triangles’ size and shape, so they can map one triangle to the other. Choices A and D use a reflection, which is not one of the stated transformations.

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