Right triangle ABC is reflected over AC, then dilated by a scale factor of . Which statements about the two triangles must be true?
None of the above.
To determine which statements about the two triangles must be true after reflecting and dilating, let's break down the process step by step:
1. Reflecting over AC: When triangle ABC is reflected over AC, the image triangle is created by flipping triangle ABC across the line AC. This means that the image triangle will have the same size and shape as the original triangle ABC, just in the opposite orientation.
2. Dilating by a scale factor: When a triangle is dilated by a scale factor, all of its sides are multiplied by the given scale factor. In this case, the scale factor is missing in the question, which makes it impossible to determine the exact size of the dilated triangle. Therefore, we cannot make any definite statements regarding the size or proportions of the dilated triangle without knowing the scale factor.
In conclusion, the only statement we can make for sure is that the image triangle, obtained after reflecting triangle ABC over AC, will have the same size and shape as the original triangle.