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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 Miles,

The final answer is Choice B. Please see explanation below and let me know if you have any further questions.

(If you found this helpful, I would greatly appreciate any feedback as I'm new to the platform, yet highly experienced in geometry).

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.

Let me know if this helped and if you have any further questions!

Thank you,

Benjamin M.

Answer 2

What aspects of a figure are maintained by a rigid translation? It's in your textbook.