Triangle Congruence: ASA and AAS — Quiz

Question 15 • Geometry

Which of these triangle pairs can be mapped to each other using a reflection and a translation?

Answer

Image with description Triangles L P K and Q R A are shown. Triangle L P K is reflected across a line to form triangle Q R A. Triangle Q R A is shifted to the right of triangle L P K. Side K P is congruent to side Q R, angle Q A R is congruent to angle K L A, and angle K P L is congruent to angle Q R A.

Image with description 2 Triangles L P K and Q R A are shown in which the side K P is congruent to side Q R, angle K P L is congruent to angle Q R A, and angle K L P is congruent to angle Q A R.

Image with description Triangles L R K and A R Q are connected at point R. Triangle L R K is reflected across point R to form triangle A R Q. RK is congruent to QR, Angle K L R is congruent to R A Q.

Image with description Triangles L P K and Q R A are shown. Triangle L P K is rotated to form triangle Q R A. Triangle Q R A is also shifted to the right. Side K P is congruent to Q R, angle L P K is congruent to angle Q R A, and angle L K P is congruent to Q A R.

Explanation

A reflection flips a figure across a line, and a translation slides it without turning it. Choice C describes triangle LPK being reflected across a line and then shifted to the right, so those are the required transformations. Choice A includes a rotation, while reflecting across a point as in D is a half-turn, not a reflection across a line.

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