Question

determine whether the polygons are similar. if they are, write a similarity statement and give the scale factor. if not, explain.

select the correct choice below and complete any answer box, if necessary, to complete your choice.
a. $rplq \sim dghe$; the simplified fraction scale factor of this polygon to $rplq$ is \\(\square\\).

Explanation:

Step1: Identify Corresponding Sides

First, we identify the corresponding sides of the two polygons. For polygon \( DGHE \) and \( RPLQ \), we look at the lengths:

• \( DG = 24 \), \( RP = 16 \)
• \( GH = 12 \), \( PL = 8 \)
• \( HE = 18 \), \( LQ = 12 \)
• \( ED = 24 \), \( QR = 16 \)

Step2: Calculate Ratios of Corresponding Sides

Now we calculate the ratios of the corresponding sides of \( DGHE \) to \( RPLQ \):

• For \( DG \) and \( RP \): \(\frac{DG}{RP}=\frac{24}{16}=\frac{3}{2}\)
• For \( GH \) and \( PL \): \(\frac{GH}{PL}=\frac{12}{8}=\frac{3}{2}\)
• For \( HE \) and \( LQ \): \(\frac{HE}{LQ}=\frac{18}{12}=\frac{3}{2}\)
• For \( ED \) and \( QR \): \(\frac{ED}{QR}=\frac{24}{16}=\frac{3}{2}\)

Since all the ratios of corresponding sides are equal (\(\frac{3}{2}\)) and the corresponding angles are equal (as indicated by the markings), the polygons are similar. The scale factor of \( DGHE \) to \( RPLQ \) is the ratio of their corresponding sides, which we calculated as \(\frac{3}{2}\).

Answer:

\(\frac{3}{2}\)