Question

independent practice
date ____ pd ____
in questions 1-3, use your understanding of similar figures to determine the corresponding angles, corresponding sides, and the scale factor. the figure on the left is the original.
similar figures

1. figure abc ~ figure def.

image of triangle abc with sides ab=18 cm, bc=18 cm, ca=16 cm; and triangle def with sides de=a cm, ef=a cm, fd=8 cm
corresponding angles and sides
angles:
∠a and ____
∠b and ____
∠c and ____
sides:
\\(\overline{ab}\\) and ____
\\(\overline{bc}\\) and ____
\\(\overline{ca}\\) and ____
scale factor
blank space

1. figure ghij ~ figure klmn.

blank space for this problem

Explanation:

Step 1: Identify Corresponding Angles

In similar triangles, corresponding angles are equal. Since \( \triangle ABC \sim \triangle DEF \), the order of the letters gives the correspondence. So \( \angle A \) corresponds to \( \angle D \), \( \angle B \) corresponds to \( \angle E \), and \( \angle C \) corresponds to \( \angle F \).

Step 2: Identify Corresponding Sides

For sides, we look at the order of the vertices. \( \overline{AB} \) (between \( A \) and \( B \)) corresponds to \( \overline{DE} \) (between \( D \) and \( E \)), \( \overline{BC} \) (between \( B \) and \( C \)) corresponds to \( \overline{EF} \) (between \( E \) and \( F \)), and \( \overline{CA} \) (between \( C \) and \( A \)) corresponds to \( \overline{FD} \) (between \( F \) and \( D \)).

Step 3: Determine Scale Factor

First, find the ratio of corresponding sides. Let's take \( AC = 16 \, \text{cm} \) and \( DF = 8 \, \text{cm} \). The scale factor from \( \triangle ABC \) to \( \triangle DEF \) is \( \frac{DF}{AC} = \frac{8}{16} = \frac{1}{2} \).

Answer:

• Angles: \( \angle A \) and \( \boldsymbol{\angle D} \), \( \angle B \) and \( \boldsymbol{\angle E} \), \( \angle C \) and \( \boldsymbol{\angle F} \)
• Sides: \( \overline{AB} \) and \( \boldsymbol{\overline{DE}} \), \( \overline{BC} \) and \( \boldsymbol{\overline{EF}} \), \( \overline{CA} \) and \( \boldsymbol{\overline{FD}} \)
• Scale Factor: \( \boldsymbol{\frac{1}{2}} \) (from \( \triangle ABC \) to \( \triangle DEF \))