Question

question 7 (multiple choice worth 1 points) (03.03r mc) if a translation maps ∠i onto ∠k, which of the following statements is true? image of a triangle jgk with a smaller triangle ghi inside, and four multiple - choice options: \\(\overline{hi} = 2\overline{jk}\\), \\(\triangle ghi \sim \triangle gjk\\), \\(\overline{gh} = 2\overline{gj}\\), \\(\angle g \cong \angle k\\)

Explanation:

Step1: Recall properties of translation

Translation is a rigid transformation. Rigid transformations preserve shape and size. So, if a translation maps \(\triangle GHI\) to \(\triangle GJK\) (since translation maps \(\angle I\) to \(\angle K\)), then \(\triangle GHI\sim\triangle GJK\) (similarity due to same - shape, and in fact congruence as translation is a rigid - motion, but similarity is a more general relation that holds for congruent figures too).

Step2: Analyze other options

• For \(\angle G\cong\angle K\): There is no information from the translation mapping \(\angle I\) to \(\angle K\) that would imply \(\angle G\cong\angle K\).
• For \(GH = 2GJ\): Translation is a rigid - motion (distance - preserving), so \(GH=GJ\) (not \(GH = 2GJ\)).
• For \(HI=2JK\): Translation is a rigid - motion (length - preserving), so \(HI = JK\) (not \(HI=2JK\)).

Answer:

\(\triangle GHI\sim\triangle GJK\)