Question

avi dilated △ade to get △abc. he marked angles in the two triangles congruent as shown. which of the following statements can be proved? options: △abc ~ △ade, ∠abc ≅ ∠acb, ∠ade ≅ ∠aed, △abc and △ade are right triangles

Explanation:

Step1: Recall Dilation and Similarity

Dilation is a transformation that produces similar figures. Similar triangles have corresponding angles congruent and corresponding sides in proportion.

Step2: Analyze Given Triangles

Since \( \triangle ADE \) is dilated to get \( \triangle ABC \), dilation preserves angle measures and creates similar triangles. So, \( \triangle ABC \sim \triangle ADE \) by the definition of similar figures (AA similarity, as we have congruent angles marked).

Step3: Evaluate Other Options

• \( \triangle ABC \) and \( \triangle ADE \) being right triangles: There's no info showing right angles.
• \( \angle ADE \cong \angle AED \): No info to support this (they aren't necessarily equal).
• \( \angle ABC \cong \angle ACB \): No info to support this (they aren't necessarily equal).

Answer:

\( \triangle ABC \sim \triangle ADE \) (the option stating \( \triangle ABC \sim \triangle ADE \))