Question

Triangle 1 is composed of line segments AB¯¯¯¯¯, BC¯¯¯¯¯, and CA¯¯¯¯¯.

Triangle 2 is composed of line segments DE¯¯¯¯¯, EF¯¯¯¯¯, and FD¯¯¯¯¯.
The triangles are similar with a scale of 3:1.

Select the true statement about the proportions of the sides.

Answer 1

`\textsf{A)} \quad \frac{m\overline{AC}}{m\overline{DF}}=3`

Explanation:

Similar Triangles

In similar triangles:

• corresponding angles are the same size.
• corresponding sides are always in the same ratio.

Given ΔABC ~ ΔDEF with a scale of 3 : 1 then:

`\bullet \quad \overline{AB} = 3\overline{DE}`

`\bullet \quad \overline{BC} = 3\overline{EF}`

`\bullet \quad \overline{AC} = 3\overline{DF}`

Therefore:

`\frac{m\overline{AC}}{m\overline{DF}}=3`