Question

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

Explanation:

Step1: Recall Similar Triangles Properties

Similar triangles have congruent corresponding angles (by definition of similarity, AA, SAS, SSS similarity criteria imply angle congruence) and proportional corresponding sides (since dilation scales lengths by a constant factor, preserving the ratio).

Step2: Analyze Transformation (Dilation)

Dilation is a similarity transformation that scales a figure. For similar triangles, after dilation (centered at origin here), angles remain congruent (dilation doesn't change angle measures), and sides become proportional (scaled by the dilation factor).

Step3: Match with Drop - Down Options

• Corresponding angles: "congruent" (as similarity requires angle congruence).
• Corresponding sides: "proportional" (since dilation scales sides by a constant ratio, making them proportional). Also, the transformation is dilation (already given in the dropdown, but for the angle and side parts: angles are congruent, sides are proportional).

Answer:

For the angle dropdown: congruent; For the side dropdown: proportional.