Question

if a right triangle △def is dilated by a scale factor of 2, which of the following statements is not true? a. △def is larger than △def. b. the sides of △def are congruent to the sides of △def. c. the angles of △def are congruent to the angles of △def. d. △def is similar to △def.

Explanation:

Step1: Recall dilation property

When a figure is dilated by a scale - factor $k = 2$, the new figure is similar to the original figure. The angles of similar figures are congruent, so the angles of $\triangle DEF$ and $\triangle D'E'F'$ are congruent (Option C is true). Also, similar figures have the same shape, so $\triangle DEF$ is similar to $\triangle D'E'F'$ (Option D is true).

Step2: Analyze side - length relationship

If a triangle $\triangle DEF$ is dilated by a scale factor of $k = 2$, the side - lengths of $\triangle D'E'F'$ are $k = 2$ times the side - lengths of $\triangle DEF$. So $\triangle D'E'F'$ is larger than $\triangle DEF$ (Option A is true). And the sides of $\triangle DEF$ are not congruent to the sides of $\triangle D'E'F'$ since the side - lengths of $\triangle D'E'F'$ are twice as long as those of $\triangle DEF$. So Option B is not true.

Answer:

B. The sides of $\triangle DEF$ are congruent to the sides of $\triangle D'E'F'$.