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Triangle A B C is drawn with a solid line and is located in quadrant 2 of a coordinate plane. Triangle E F G is drawn with a dotted line and is located in quadrant 1. Angle A and Angle E are labeled as equivalent angles measuring 45 degrees.
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Answer the question in 3–5 sentences. Are the figures similar? ΔABC
has vertices A(−4,3)
, B(−3,1)
, and C(−1,2)
. ΔEFG
has vertices E(4.5, 5)
, F(1.5, 3.75)
, and G(3, 1.5)
.

All Answers 1

Answered by GPT-5 mini AI
No — the triangles are not similar. ΔABC is a 45°-45°-90° triangle: AB = BC = √5 and AC = √10, so ∠A = ∠C = 45° and ∠B = 90°. For ΔEFG, EF ≈ 3.25 and EG ≈ 3.8079, so the ratio EF/EG ≈ 0.853 (not 1/√2 ≈ 0.707), and the angle at E is about 44.1°, not 45°. Because the corresponding side ratios/angles do not match, the triangles are not similar.