Ratios/Proportions/Similar Figures Study Guide
Name:___________________
Date:________________
Class:________________
Ratios:
A ratio is a comparison of two quantities by division.
● Three ways to write ratios
○ a to b,
○ a:b,
○ ab
Example: If there are 35 girls and 28 boys, the ratio of girls to boys can be written as:
● 35 to 28
● 35:28
● 35
28
Proportions:
Proportions are ratios that are equal to each other.
● To determine if two ratios are proportional you can;
○ Simplify both and see if they are equivalent, or
○ Cross multiply the numerators and denominators and see if you get the same product.
Example: Determine if the two ratios form a proportion.
14 = 20
21
30
14 = 2 , 20 = 2
Simplify:
21
3
30
3
Are the simplified ratios equivalent?
Yes, the ratios are proportional.
______________________________________________________________________________
14 = 20
Cross Multiply:
21
30
Multiply numerators times denominators
14 x 30 = 420, 21 x 20 = 420
Are the cross products equal?
Yes, the ratios are proportional.
Determine by simplifying or using cross products if the two ratios are proportional.
1.
4
7
2.
39
45
& 52
72
3.
16
56
& 12
42
Are the ratios equivalent?
Are the ratios proportional?
Cross Multiply
Are the products
equivalent?
Are the ratios proportional?
& 28
49
4.
10
25
& 28
70
5.
15
20
& 10
15
6.
8
9
& 64
81
Solving Proportions:
1
Simplify Ratios
To solve a proportion​,
1. Cross multiply the numerators and denominators.
2. Divide to solve for the variable.
Example: Solve the proportion
x
21
= 38
42
1. Cross Multiply (Numerators times Denominators)
2. Multiply
3. Divide
42x = 21(38)
42x​ = ​798
42
42
x = 19
Solve each proportion:
7.
13
60
=
52
d
8.
w
12
=
16
4
9.
r
45
=
15
18
10.
27
n
=
36
88
size.
●
●
Example:
Rectangle A is similar to Rectangle B because:
Both rectangle have 4 90 degree angles (corresponding angles are congruent)
A
8
2
The ratio of sides from Rectangle
Rectangle B = 4 = 1 = 2
Example 2:
2
Determine if the triangles are similar.
Are the ratios of corresponding sides equivalent?
10
8
= 86 = 12
10
5 = 4 = 6
Simplify the ratios:
4
3
5
Since all the ratios are not equivalent, the figures are
not similar.
Are these figures similar?
Yes/No
Explain
11.
12.
13.
Use proportions to find the missing measurement.
14.
CJ is 5 ft tall and casts a 7 ft shadow. If a nearby tree casts a 14 ft shadow, how tall is the
tree?
3