Question

1. here are two triangles.

what is the length of segment df?
(careful that you are matching correct corresponding sides)

1. the triangle abc is taken to triangle abc by

(the image shows two triangles with angle and side labels, and some handwritten equations and a final answer of 13.5 for df)

Explanation:

Step1: Identify Similar Triangles

Triangles \(ABC\) and \(DEF\) are similar (same angles: \(44^\circ\), \(68^\circ\), \(44^\circ\)). Corresponding sides: \(AB = 8\) corresponds to \(DE = 18\), \(AC = 6\) corresponds to \(DF = x\).

Step2: Set Up Proportion

For similar triangles, \(\frac{AB}{DE}=\frac{AC}{DF}\), so \(\frac{8}{18}=\frac{6}{x}\).

Step3: Solve for \(x\)

Cross - multiply: \(8x = 6\times18\). Calculate \(6\times18 = 108\), so \(8x=108\). Divide both sides by 8: \(x=\frac{108}{8}=13.5\).

Answer:

The length of segment \(DF\) is \(13.5\).