Question

triangles abc and dec, graphed on the coordinate plane, are similar triangles. how can a transformation be used to justify that similar? complete the sentences by selecting the correct op - down menus. triangle dec is the image of △abc after a choose centered at the origin. that transformation shows that △abc∼△dec because all the corresponding angles are choose and all the corresponding sides are choose. the dropdown options include rotation, reflection, translation, dilation. the graph shows triangles on a coordinate plane with points d, e, c, a, b.

Explanation:

Step1: Analyze Transformation Type

To show similarity, dilation (scaling) is key. Dilation changes size but not shape, preserving angle measures and creating proportional sides. Rotation, reflection, translation preserve size/shape (congruence), but here DEC is larger, so dilation.

Step2: Angle and Side Properties

After dilation, corresponding angles remain equal (since dilation preserves shape), and corresponding sides are proportional (as dilation scales lengths by a factor).

Answer:

First dropdown: dilation
Second (center): origin (implied, as dilation centered at origin here)
Third dropdown: equal
Fourth dropdown: proportional