Proportions
A recipe uses 2 cups of flour to make 8 cookies. How many cups of flour are needed to make 24 cookies?
6 Cups?
A drawing is enlarged from 4 inches wide to 12 inches wide. What is the scale factor?
1:3
A tree casts a 12-foot shadow. At the same time, a 6-foot person casts a 4-foot shadow.
How tall is the tree?
18 Feet
This is a method used to find a size, height, or distance by calculating related values instead of measuring it directly.
Indirect measurement
Determine whether this relationship is proportional:
Tickets Cost
1 $8
2 $16
3 $32
4 $40
Yes
A rectangle measures 8 ft × 5 ft. A scale model uses a scale factor of ½. What are the dimensions of the model?
4 ft × 2.5 ft
A student stands 5 feet tall and casts a 3-foot shadow. A nearby building casts a 24-foot shadow.
How tall is the building?
40 feet
Two triangles with congruent corresponding angles and proportional corresponding sides are called what?
Similar triangles
A car travels 180 miles using 6 gallons of gas. At the same rate, how far can it travel using 11 gallons?
330 Miles
A blueprint uses the scale 1 inch = 8 feet. A bedroom is 2.5 inches long on the blueprint. How long is the actual bedroom?
20 feet
A flagpole casts a 15-foot shadow. At the same time, a 4-foot-tall sign casts a 2.5-foot shadow.
How tall is the flagpole?
24 Feet
A relationship with a constant ratio between corresponding values is a what?
Proportional relationship
A student says that a 3:1 ratio always means a relationship is proportional. Is the student correct? Explain.
No. A single ratio does not prove proportionality. The ratio must remain constant between corresponding quantities.
A photograph is 800 × 600 pixels. It is enlarged by a scale factor of 1.5.
What are the new dimensions?
1,200 × 900 pixels
You cannot measure the width of a river directly. You create two similar triangles.
On your side of the river:
Set up a proportion and determine the width of the river.
X/30=18/12 x=45
This occurs when one quantity increases or decreases at a constant rate with another quantity.
Direct proportion
A store sells shirts for $18 each. However, there is a $7 shipping fee for every order, regardless of how many shirts are purchased.
Is the relationship between the number of shirts and total cost proportional? Explain why or why not.
No. The $7 fixed fee means the relationship does not pass through the origin.
A rectangular patio is 12 ft by 18 ft. A model is created using a scale factor of ¼.
What is the area of the original patio and the area of the model?
Original: 216 ft²
Model: 13.5 ft²
A student wants to determine the height of a building. A 6-foot pole casts a 4-foot shadow. At the same time, the building casts a 36-foot shadow.
The student measures the building's shadow from the edge of the building to the end of the shadow, but the building is on a 3-foot raised platform.
What is the height of the building above the platform?
54 feet
This occurs when one quantity increases while the other decreases so their product stays constant.
Inverse proportion