Question

question 10 (multiple choice worth 1 points) (01.024 mc) decide whether the triangles are similar. if so, determine the appropriate expression to solve for x. the triangles are not similar, no expression for x can be found. δabc - δdcf, x = r w/u. δabc - δefd, x = r w/z. δabc - δfde, x = z * w/r.

Explanation:

Step1: Find angles in triangles

In \(\triangle ABC\), \(\angle B=180^{\circ}-53^{\circ}-62^{\circ}=65^{\circ}\). In \(\triangle DEF\), \(\angle E = 180^{\circ}-65^{\circ}-53^{\circ}=62^{\circ}\).

Step2: Determine similar - triangles

Since \(\angle A=\angle F = 53^{\circ}\), \(\angle B=\angle D=65^{\circ}\), and \(\angle C=\angle E = 62^{\circ}\), \(\triangle ABC\sim\triangle FDE\) (by AA - similarity criterion).

Step3: Set up proportion

For similar triangles \(\triangle ABC\) and \(\triangle FDE\), the ratios of corresponding sides are equal. That is \(\frac{w}{z}=\frac{x}{r}\), so \(x = r\cdot\frac{w}{z}\).

Answer:

\(\triangle ABC\sim\triangle FDE,x = r\cdot\frac{w}{z}\)