Question

Triangle ABC is mapped to Triangle A²B²C² by a translation. Which relationship is not true?

Responses
a. AA’ || BB’
b. AB’ || A’B
c. BC = B’C’
d. AA’ = CC’

Answer 1

In a translation, corresponding sides and angles remain congruent. The relationship that is not true is b. AB’ || A’B, since AB’ and A’B are not corresponding segments and do not have to be parallel.

Step-by-step explanation:

The question asks which relationship is not true when Triangle ABC is mapped to Triangle A²B²C² by a translation. In a translation, all points of the original figure move the same distance in the same direction. This means that corresponding sides and angles of the original and image triangles will remain congruent.

• a. AA’ || BB’: This is true. In a translation, corresponding lines remain parallel.
• b. AB’ || A’B: The segments AB’ and A’B are not necessarily parallel, as they are not corresponding segments of triangles ABC and A²B²C².
• c. BC = B’C’: This is true. Side BC of Triangle ABC will be congruent to side B’C’ of Triangle A²B²C² because of the properties of a translation.
• d. AA’ = CC’: This is true. The lengths of the segments connecting corresponding vertices will be the same as these are the paths of translation.

Therefore, the relationship that is not true is b. AB’ || A’B.