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Which similarity criterion proves the two triangles above are similar?

(1 point)
Responses
ABC (-3, -2), (4, -2), (-3,3) to A' B' C' (-6, -2), (8, -2), (-6,8) This is a dilation enlargement
AA~
AA~

SSS~
SSS~

SAS~
SAS~

AAS~
AAS~
Question 2

1 answer

To determine the similarity criterion that proves triangles ABC and A'B'C' are similar, we need to analyze the coordinates provided for both triangles.

The coordinates are:

  • Triangle ABC: A(-3, -2), B(4, -2), C(-3, 3)
  • Triangle A'B'C': A'(-6, -2), B'(8, -2), C'(-6, 8)

From the coordinates, we can observe the following:

  1. The x-coordinates of points A and A' have a ratio of \(-6 / -3 = 2\).
  2. The x-coordinates of points B and B' have a ratio of \(8 / 4 = 2\).
  3. The x-coordinates of points C and C' have a ratio of \(8 / 3 = 2\).

All corresponding x-coordinates have the same ratio of 2, which indicates that the triangles are similar by the criterion of SSS~ (Side-Side-Side), because the lengths of corresponding sides of triangles A and A' are proportional.

Thus, the correct response for the similarity criterion that proves the two triangles are similar is:

SSS~ (Side-Side-Side Similarity).