To prove that triangles ABC and A'B'C' are similar using the Side-Angle-Side (SAS) similarity criterion, we can show that two pairs of corresponding sides are in proportion and the angle between them is the same. The length of side AB is the distance between points A(-3,-2) and B(4,-2), which is 7 units, and the length of side A'B' is the distance between points A'(-6,-2) and B'(8,-2), which is also 14 units. Thus, the ratio of AB to A'B' is 7:14 or 1:2. Similarly, the length of side AC (from A to C) is 5 units, while side A'C' (from A’ to C’) is 10 units. The ratio of AC to A'C' is also 5:10 or 1:2. Since the sides are in proportion and the angles between the sides are the same (both triangles are horizontal across the same segment), by SAS, triangle ABC is similar to triangle A'B'C'.
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.
a (-3,-2)
a'(-6, -2)
b (4,-2)
b'(8,-2)
c(-3,3)
c'(-6,8)
1 answer
1 answer