Question for Geometry

Question

Triangle ABC is mapped to Triangle A′B′C′ by a translation. Which relationship is not true?

A. AA′∥BB′

B. AB′∥A′B

C. BC≅B′C′

D. AA′≅CC′

Answer 1

Hi Christine,

In the case of a translation, corresponding sides are parallel and congruent. Here's how each choice relates to this:

Choice A: AA' is parallel to BB' - This is true because in a translation, corresponding sides are parallel.

Choice B: AB' is parallel to A'B - This is not true. AB' and A'B are not corresponding sides, so we can't say they are parallel.

Choice C: BC is congruent to B'C' - This is true. In a translation, corresponding sides are congruent.

Choice D: AA' is congruent to CC' - This is true. The distance between each point and its corresponding point is constant in a translation.

So the statement that is not true is Choice B: AB' is parallel to A'B.

Hope this helped! Let me know if you have any other questions.

Thank you,

Benjamin M.

p.s. Any feedback/review is very helpful since I am new to Wyzant (yet experienced in geometry!)

Answer 2

Consider the triangle with vertices A(x_A, y_A), B(x_B, y_B), and C(x_C, y_C). If we translate that triangle, then we are moving all the points on it by a fixed horizontal distance of h units and a fixed vertical distance of v units. This produces a new triangle with vertices A'(x_A + h, y_A + v), B'(x_B + h, y_B + v), and C'(x_C + h, y_C + v). Two questions arise naturally,

1. Does this action preserve length?
2. Does this action preserve slope?

To answer the first question, we may compare the lengths AB and A'B'. If they are equal, then AB will be congruent to A'B'. A quick calculation using the distance formula will provide us with the answer.

To answer the second question, we need only compute the slopes of AB and A'B'. If they are equal, then AB will be parallel to A'B'