Question

question 11 of 40
if an isosceles triangle $\triangle abc$ is dilated by a scale factor of 3, which of the following statements is not true?
a. $\triangle abc$ is larger than $\triangle abc$.
b. the sides of $\triangle abc$ are congruent to the sides of $\triangle abc$.
c. $\triangle abc$ is similar to $\triangle abc$.
d. the angles of $\triangle abc$ are congruent to the angles of $\triangle abc$.

Explanation:

Step1: Recall dilation properties

Dilation with scale factor $k>1$ enlarges the figure. Corresponding sides are scaled by $k$, angles remain congruent, and the resulting figure is similar to the original.

Step2: Analyze each option

• Option A: Scale factor 3 > 1, so $\triangle A'B'C'$ is larger. True.
• Option B: Sides of $\triangle ABC$ are scaled by 3 to get $\triangle A'B'C'$, so sides are not congruent. False.
• Option C: Dilation preserves shape, so triangles are similar. True.
• Option D: Dilation preserves angle measures, so angles are congruent. True.

Answer:

B. The sides of $\triangle ABC$ are congruent to the sides of $\triangle A'B'C'$