Download Midsegments of Triangles

Ratios and Proportions
Name_____________________________
Ratio - Comparison of two quantities by division.
a

b
 a:b
 a to b
(where b ≠ 0)
Usually a and b are in the same units and in simplest form.
Extended ratio – Compares 3 or more numbers.
 a:b:c
Proportion – An equation that states two ratios are equivalent.
a c

b d
Extremes – a and d
Means – b and c
In a proportion, the product of the means is equal to the product of the extremes.
When using ratios…..
If you know only part:
1. Set up a proportion
2. Put the like quantities across
from each other
3. Solve…this will give you the
other part
If you know a total:
1. Make a Let statement and put
an X after each number in the ratio
2. Add them to equal the total
3. Solve for x
4. Substitute x in to find the value
1. What is the solution to each proportion?
6 5

a)
x 4
b)
y4 y

9
3
2. A bonsai tree is 18 in. wide and stands 2 ft tall. What is the ratio of the width of the bonsai
to its height?
3. Two complementary angles in the ratio of 2:3. The larger angle measures 54°. Find the
measure of the smaller angle.
4. The lengths of the sides of a triangle are in the extended ratio 3:5:6. The perimeter of the
triangle is 98 in. What is the length of the longest side?
5. In the diagram,
a)
x

y
b)
6

x
c)
y7

7
x y
 . What ratio completes the equivalent proportions?
6 7