Question

consider the transformation shown. use the drop-down menus to complete the sentence. the transformation is dropdown because the dropdown preserved. pre - image: a right triangle with side lengths 6, 8, 10 (right angle and two other angles marked). image: a right triangle with side lengths 3, 4, 5 (same angles marked, labeled image).

Explanation:

Step1: Analyze side ratios

Check the ratios of corresponding sides. Pre - image sides: 6, 8, 10. Image sides: 3, 4, 5.
$\frac{6}{3} = 2$, $\frac{8}{4}=2$, $\frac{10}{5} = 2$. So the scale factor is 2 (reduction by factor 1/2).

Step2: Analyze angles

Both triangles have a right angle and the other angles (marked with arcs) should be equal because of similar triangles property. In similar transformations, angles are preserved.

Step3: Identify transformation

A transformation that preserves angle measures and has proportional side lengths is a similarity transformation (specifically a dilation here, but similarity includes dilation). The key is that angles are preserved (and side ratios are constant). So the transformation is a similarity transformation (or dilation) because the angle measures (or shape, or angle - angle - angle similarity) are preserved.

Answer:

The transformation is \(\boldsymbol{\text{a similarity transformation (or dilation)}}\) because the \(\boldsymbol{\text{angle measures (or shape)}}\) preserved.

(Note: If the drop - down options have "similarity" or "dilation" for the first blank and "angle measures" or "shape" for the second, these would be the appropriate choices. For example, if options are like first drop - down: "a similarity transformation", "a translation", "a rotation"; second drop - down: "angle measures", "side lengths (exact)", "position". Then the first is "a similarity transformation" and the second is "angle measures" since side lengths are scaled (not preserved exactly) but angles are.)