Question

find the missing length. the triangles in each pair are similar.

1. $\triangle abc \sim \triangle agf$

23)
solve for $x$. the polygons in each pair are similar
d) similar; sas similarity
c) similar; aa similarity

Explanation:

Step1: Identify Proportions from Similar Triangles

Since \( \triangle ABC \sim \triangle AGF \), corresponding sides are proportional. So, \( \frac{AC}{AF} = \frac{AB}{AG} \). Let \( AC = x \) (the missing length), \( AF = 18 \), \( AB = 50 \), \( AG = 15 \).

Step2: Set Up the Proportion Equation

Substitute values into the proportion: \( \frac{x}{18} = \frac{50}{15} \).

Step3: Solve for \( x \)

Cross - multiply: \( 15x = 50\times18 \). Calculate \( 50\times18 = 900 \). Then \( x=\frac{900}{15}=60 \).

Answer:

The missing length (AC) is 60.