Question

Right triangle ABC is reflected over the line AC then dilated by a scale factor 2/3 to form triangle DEZ. Which statements about the two triangles must be true?

A. DEZ is similar to ABC.
B. DEZ is congruent to ABC.
C. DEZ has a smaller area than ABC.
D. DEZ has a larger perimeter than ABC.

Answer 1

Triangle DEZ is similar to ABC, not congruent to it, has a smaller area, and also a smaller perimeter than triangle ABC.

Step-by-step explanation:

When right triangle ABC is reflected over the line AC and then dilated by a scale factor of 2/3 to form triangle DEZ, several statements about the relationships between the triangles can be made:

• Triangle DEZ is similar to triangle ABC because reflections and dilations are both transformations that preserve shape but not necessarily size.
• Triangle DEZ is not congruent to triangle ABC since it has been dilated by a scale factor of 2/3, changing its size.
• Triangle DEZ has a smaller area than triangle ABC due to the dilation factor of 2/3. Since the area of a triangle is proportional to the square of its sides, the area would be (2/3)² or 4/9 the area of the original triangle.
• Triangle DEZ also has a smaller perimeter than triangle ABC, because the sides of DEZ are 2/3 the length of the corresponding sides in triangle ABC.