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.

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 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(1.6,1.8)
, and G(3,1.5)
. Is ΔEFG
the image of ΔABC
?

Answer 1

The figures are similar because they have two corresponding angles that are congruent. However, the figures are not congruent because their corresponding sides are not proportional. The rotation and translation of ΔABC would result in a different set of coordinates for the vertices, making ΔEFG not the exact image of ΔABC.