Question

date:
this is a 2 - page document!
directions: determine whether the figures below are similar. prove your answer
1.
2.
3.
4.
5.
6.

1. if the figures below are similar, give the scale factor of figure a to figure b.
2. if the figures below are similar, give the scale factor of figure b to figure a.

directions: each pair of figures are similar. use a proportion to find the missing side.
similar figures work and solution
9.
10.

Explanation:

Step1: Check similarity for Q1

Compare side ratios:
$\frac{5}{10}=\frac{1}{2}$, $\frac{12}{24}=\frac{1}{2}$, $\frac{13}{26}=\frac{1}{2}$
All ratios equal, so similar.

Step2: Check similarity for Q2

Compare side ratios:
$\frac{15}{9}=\frac{5}{3}$, $\frac{24}{12}=2$
Ratios not equal, so not similar.

Step3: Check similarity for Q3

Compare side ratios:
$\frac{6}{9}=\frac{2}{3}$, $\frac{10}{15}=\frac{2}{3}$, $\frac{14}{21}=\frac{2}{3}$
All ratios equal, so similar.

Step4: Check similarity for Q4

Compare side ratios:
$\frac{16}{12.8}=\frac{5}{4}$, $\frac{30}{24}=\frac{5}{4}$
All ratios equal, so similar.

Step5: Check similarity for Q5

Compare side ratios:
$\frac{6}{9}=\frac{2}{3}$, $\frac{10}{12}=\frac{5}{6}$
Ratios not equal, so not similar.

Step6: Check similarity for Q6

Compare side ratios:
$\frac{24}{12}=2$, $\frac{16}{12.8}=\frac{5}{4}$
Ratios not equal, so not similar.

Step7: Find scale factor Q7

Scale factor A to B:
$\frac{2}{8}=\frac{1}{4}$, $\frac{6}{24}=\frac{1}{4}$

Step8: Find scale factor Q8

First confirm similarity: $\frac{12}{10}=\frac{6}{5}$, $\frac{15}{8}
eq\frac{6}{5}$ → Not similar, so no valid scale factor.

Step9: Solve for x in Q9

Set up proportion:
$\frac{9}{x}=\frac{12}{20}$
Cross multiply: $12x=9\times20$
$x=\frac{180}{12}=15$

Step10: Solve for x in Q10

Set up proportion:
$\frac{x}{6}=\frac{25}{15}$
Cross multiply: $15x=25\times6$
$x=\frac{150}{15}=10$

Answer:

1. Similar (all side ratios = $\frac{1}{2}$)
2. Not similar (side ratios $\frac{5}{3}$ and 2, not equal)
3. Similar (all side ratios = $\frac{2}{3}$)
4. Similar (all side ratios = $\frac{5}{4}$)
5. Not similar (side ratios $\frac{2}{3}$ and $\frac{5}{6}$, not equal)
6. Not similar (side ratios 2 and $\frac{5}{4}$, not equal)
7. $\frac{1}{4}$
8. Not similar, no valid scale factor
9. $x=15$
10. $x=10$