Question

Each pair of polygons is similar. Write a similarity statement, find x, the measures of the indicated sides, and the scale factor. Problem 18

Answer 1

For figure 18:

• Similarity Statement:

If two pairs of corresponding sides are in proportion, and the included angle of each pair is equal, then the two triangles they form are similar (SAS postulate).

• Scale factor (considering smaller figure is enlarged to the bigger one):

$\frac{6}{4}=\frac{3}{2}$

• To find x:

$\frac{12-x}{x+7}=\frac{3}{2}=1.5$$\begin{gathered} 24-2x=3x+21 \\ 3=5x \\ \\ x=\frac{3}{5}=0.6 \end{gathered}$

• To find missing sides:

AC = x + 7 = 3/5 + 7 = 7.6

CE = 12 - x = 11.4