Question

Triangle upper A upper B upper C has vertices located at the following points: upper A at left parenthesis negative 3 comma negative 2 right parenthesis, upper B at left parenthesis 4 comma negative 2 right parenthesis, and upper C at left parenthesis negative 3 comma 3 right parenthesis. Triangle upper A prime upper B prime upper C prime has vertices located at the following points: upper A prime at left parenthesis negative 6 comma negative 2 right parenthesis, upper B prime at left parenthesis 8 comma negative 2 right parenthesis, and upper C prime at left parenthesis negative 6 comma 8 right parenthesis.


Using any of the three triangle similarities of corresponding angles or side lengths, explain in 1–2 sentences why the two triangles are similar. Reference the triangle similarity criteria of choice (SAS, SSS, or AA) and explain your reasoning in your answer.

(2 points)

Answer 1

Use SSS: AB = 7, AC = 5, BC = sqrt(74), while A′B′ = 14, A′C′ = 10, B′C′ = 2·sqrt(74), so each side of ΔA′B′C′ is exactly 2 times the corresponding side of ΔABC. Therefore the triangles are similar by the SSS similarity criterion (scale factor 2).