Triangle LQA is the same size as triangle PBK but Triangle LQA is down and to the right of triangle PBK.

Question

To prove the triangle are congruent, which of the following rigid motions would map triangle PBK to triangle LQA?
A. translations along the vector so that point B maps to point Q
B. rotation of 180 degrees counterclockwise about point B
C. translation along the vector so that point B maps to point A
D. translation along the vector so that point P maps to point A

Answer 1

To determine which rigid motion maps triangle PBK to triangle LQA, we can analyze the situation based on the information provided. Since triangle LQA is the same size as triangle PBK and is located down and to the right of triangle PBK, a translation is the most likely candidate to connect the two triangles directly.

Let’s examine each option:

A. translations along the vector so that point B maps to point Q:

• This seems plausible because it directly indicates a translation that might align triangle PBK's point B with triangle LQA's corresponding point Q.

B. rotation of 180 degrees counterclockwise about point B:

• This would change the orientation of the triangle and is not suitable since we need direct congruence (no flipping).

C. translation along the vector so that point B maps to point A:

• This option would not work correctly if A and Q are different points, as you are attempting to position B on A.

D. translation along the vector so that point P maps to point A:

• Similar to option C, mapping P to A might not correctly position triangle PBK in relation to LQA.

Given this analysis, the most appropriate answer is:

A. translations along the vector so that point B maps to point Q.

This option suggests a direct translation, which preserves the triangle's size and shape, effectively mapping triangle PBK to triangle LQA congruently.