After being reduced by a scale factor of , the resulting triangle has the side lengths of 8, 12, and 16. 2 5 What are the side lengths of the original triangle?
Which of the following statements is true regarding the corresponding angles in the new triangle? Justify your reasoning. A. The corresponding angles remain the same. B. The corresponding angles have been reduced by . 2/5 C. The corresponding angles have been scaled by . 5/2 D. The corresponding angles are halved.
To find the side lengths of the original triangle, we need to "undo" the scale factor of 2/5 on the new triangle. This means we need to multiply each side length of the new triangle (8, 12, 16) by 5/2.
So, the side lengths of the original triangle are:
5/2 * 8 = 20
5/2 * 12 = 30
5/2 * 16 = 40
Therefore, the side lengths of the original triangle are 20, 30, and 40.
Regarding the corresponding angles in the new triangle, the correct statement is:
B. The corresponding angles have been reduced by 2/5.
This is because when a triangle is reduced by a scale factor, all corresponding angles remain congruent. So, the corresponding angles in the new triangle are not the same as in the original triangle, but they have been reduced by the same scale factor of 2/5.