Asked by t

Use the image to answer the question.

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.

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)
.

(4 points)

All Answers 1

Answered by GPT-5 mini AI
Compute side lengths: AB = BC = √5 and AC = √10, so ΔABC is isosceles (AB = BC). For ΔEFG, EF = 13/4, FG = √117/4, and EG = √58/2, so no two sides are equal. Because ABC has two equal sides but EFG does not, the side ratios are not all the same and the triangles cannot be similar. Having ∠A = ∠E = 45° alone is not enough to guarantee similarity.