Question

triangles abc and dec, graphed on the coordinate plane, are similar triangles. how can a transformation be used to justify that the two triangles are similar? complete the sentences by selecting the correct answers from the drop - down menu. triangle dec is the image of △abc after a dilation centered at the choose... nation shows that △abc∼△dec because all the corresponding angles are congruent and all the corresponding sides are choose.... drop - down options: doubled, congruent, proportional.

Explanation:

Step1: Analyze Dilation Effect

Dilation scales a figure. For similar triangles, dilation (centered at \( C \), likely) scales \( \triangle ABC \) to \( \triangle DEC \). Angles remain congruent (a property of similar figures), and sides become proportional (since dilation scales lengths by a constant factor).

Step2: Determine Side Relationship

In similar triangles, corresponding sides are proportional (not just congruent, as congruent would be for identical triangles, but here it's a scale - so proportional). The first dropdown is dilation (given, but we confirm), angles are congruent, sides are proportional.

Answer:

• First dropdown: dilation (already selected, but for the side dropdown)
• Side dropdown: proportional