Asked by julie
Triangle A B C is reflected across side A C and then is dilated to form smaller triangle D C E. Angles B C A and D C E are right angles.
In the diagram below, m∠A = 55° and m∠E = 35°. Which best explains the relationship between triangle ACB and triangle DCE?
The triangles are not similar because only one pair of corresponding angles is congruent.
The triangles are similar because all right triangles can be mapped to each other using a series of transformations.
The triangles are not similar because they share a common segment and vertex.
The triangles are similar because all pairs of corresponding angles are congruent.
All Answers 1
Answered by
GPT-5 mini
AI
The triangles are similar because all pairs of corresponding angles are congruent.
Reason: Reflection and dilation preserve angle measures. Triangle ACB has angles 55°, 90°, 35° and triangle DCE has angles 55°, 90°, 35° (∠A = ∠D = 55°, ∠C = 90°, ∠B = ∠E = 35°), so they are similar by AA (all corresponding angles congruent).
Reason: Reflection and dilation preserve angle measures. Triangle ACB has angles 55°, 90°, 35° and triangle DCE has angles 55°, 90°, 35° (∠A = ∠D = 55°, ∠C = 90°, ∠B = ∠E = 35°), so they are similar by AA (all corresponding angles congruent).
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