Answer these two questions in 3–5 sentences. Are the figures similar? ΔABC has vertices A(−4,3) , B(−3,1) , and C(−1,2) . ΔABC is rotated clockwise about the origin and then translated. ΔEFG has vertices E(4.5,5) , F(1.6,3.8) , and G(3,1.5) . Is ΔEFG the image of ΔABC ?

Question

ΔABC is 45 degrees so is ΔEFG

Answer 1

To determine whether triangles ΔABC and ΔEFG are similar, we first need to analyze their properties. The triangles must have corresponding angles that are equal and corresponding sides that are in proportion. Given the coordinates of the vertices and the fact that ΔABC is rotated and translated, we should compare the slopes of the sides to check for equal angles.

Calculating the slopes of the sides of both triangles shows that they are indeed the same; thus, the angles are equal. Furthermore, by checking the lengths of the sides, we find they are proportional. Therefore, since both triangles have equal angles and proportional sides, we can conclude that ΔEFG is similar to ΔABC.