Question

A(15m) Lesson Quiz -onsAre the polygons similar? If they are, write a similarity statement and give the scale factor.PA12G101215N15SO Yes. POSN~ KDAG, scale factor is 5:4O Yes. POSN~ KDAG, scale factor is 4:507.56D8

Answer 1

Answer

Yes. POSN~KDAG, scale factor is 5:4

Step-by-step explanation

From the diagram, the following pairs of angles are congruent:

$\begin{gathered} \angle P\cong\operatorname{\angle}K \\ \operatorname{\angle}S\operatorname{\cong}\operatorname{\angle}A \\ \operatorname{\angle}N\operatorname{\cong}\operatorname{\angle}G \end{gathered}$

Then, the next quadrilaterals can be similar:

$POSN\sim KDAG$

If these quadrilaterals are similar then the ratio between their corresponding sides must be constant.

$\begin{gathered} \frac{PO}{KD}=\frac{10}{8}=\frac{5}{4} \\ \frac{OS}{DA}=\frac{7.5}{6}=\frac{5}{4} \\ \frac{SN}{AG}=\frac{15}{12}=\frac{5}{4} \\ \frac{PN}{KG}=\frac{15}{12}=\frac{5}{4} \end{gathered}$

In conclusion, POSN is similar to KDAG and the scale factor is 5:4