Question

select the correct answer from each drop - down menu. consider $\triangle efg$ and $\triangle hij$. triangle hij is \\(\boldsymbol{\downarrow}\\) triangle efg. since triangle efg uses \\(\boldsymbol{\downarrow}\\) to map onto triangle hij. the options for the first drop - down: a rotation and dilation of, a translation and dilation of, a reflection of, a translation and reflection of. the options for the second drop - down: only rigid transformations

Explanation:

Step1: Analyze Triangle Congruence

Triangles \( \triangle EFG \) and \( \triangle HIJ \) have congruent markings (same number of tick marks on sides), so they are congruent. Rigid transformations (rotation, reflection, translation) preserve congruence; dilation changes size, so dilation is not involved.

Step2: Identify Transformation Type

Looking at the orientation and position, a reflection (flips the figure) can map \( \triangle EFG \) to \( \triangle HIJ \) considering the side markings and angle positions. Also, rigid transformations (rotation, reflection, translation) are used since there's no dilation (sides remain same length, so no scaling).

Answer:

First drop - down: a reflection of; Second drop - down: only rigid transformations