Question

assignment: page 96
the triangles in each pair are similar; identify the congruent corresponding angles
and the corresponding proportional side lengths.
① δabc is similar to δabc.
⑨ δdef is similar to δdef.
8 multiple answer 2 points
a. choose all of the statements that are true about the figures. select all that apply
□ ∠b ≅ ∠b
□ $\frac{ab}{ac} = \frac{bc}{ba} = \frac{ac}{ab}$
□ $\frac{ab}{ab} = \frac{bc}{bc} = \frac{ac}{ac}$
□ ∠c ≅ ∠c
□ ∠a ≅ ∠a
9 multiple choice 1 point
b. which statement is not true about the figures?
○ $\frac{de}{de} = \frac{ef}{ef} = \frac{df}{df}$
○ ∠d ≅ ∠e
○ ∠f ≅ ∠f
○ ∠d ≅ ∠d

Explanation:

Part a (Multiple Answer)

1. For similar triangles, corresponding angles are congruent. So \( \angle B \cong \angle B' \), \( \angle C \cong \angle C' \), \( \angle A \cong \angle A' \) are true (corresponding angles of similar triangles are equal).
2. The ratio of corresponding sides of similar triangles is equal. If \( \triangle ABC \sim \triangle A'B'C' \), then \( \frac{A'B'}{AB}=\frac{B'C'}{BC}=\frac{A'C'}{AC} \) (correct ratio of corresponding sides), while \( \frac{A'B'}{AC}=\frac{B'C'}{BA}=\frac{A'C'}{AB} \) is incorrect as it does not match corresponding sides.

1. For similar triangles \( \triangle DEF \sim \triangle D'E'F' \):

• \( \frac{D'E'}{DE}=\frac{E'F'}{EF}=\frac{D'F'}{DF} \) is true (ratio of corresponding sides).
• \( \angle F \cong \angle F \) is true (common angle or corresponding angle).
• \( \angle D \cong \angle D \) is true (corresponding angle of similar triangles).
• \( \angle D \cong \angle E \): There is no reason for \( \angle D \) and \( \angle E \) to be congruent (they are not necessarily equal in a triangle, and similarity does not imply this).

Answer:

• \( \boldsymbol{\angle B \cong \angle B'} \)
• \( \boldsymbol{\frac{A'B'}{AB}=\frac{B'C'}{BC}=\frac{A'C'}{AC}} \)
• \( \boldsymbol{\angle C \cong \angle C'} \)
• \( \boldsymbol{\angle A \cong \angle A'} \)

Part b (Multiple Choice)