Question

a dilation with center (0, 0) and scale factor of 2 maps $\triangle abc$ to $\triangle def$. which best compares $m\angle b$ to $m\angle e$? a. $m\angle b = 2(m\angle e)$ b. $m\angle e = 2(m\angle b)$ c. $m\angle b = m\angle e$ d. $m\angle e = 180 - m\angle b$

Explanation:

Step1: Recall Dilation Properties

Dilation is a transformation that scales a figure but preserves the shape, meaning corresponding angles of similar figures (formed by dilation) are congruent. So, in similar triangles \(\triangle ABC\) and \(\triangle DEF\) (from dilation), corresponding angles \(\angle B\) and \(\angle E\) should have equal measures.

Step2: Analyze Options

• Option A: Suggests \(m\angle B = 2(m\angle E)\), which contradicts angle congruence in similar figures.
• Option B: Suggests \(m\angle E = 2(m\angle B)\), also contradicts angle congruence.
• Option C: States \(m\angle B = m\angle E\), which matches the property of similar figures (angles are congruent in dilation).
• Option D: Suggests supplementary angles, which is incorrect for corresponding angles in dilation.

Answer:

C. \( m\angle B = m\angle E \)