1. 7-1 Vocabulary
Ratio
Proportion
Extremes
Means
Cross products

2. 7-1 Ratio and Proportion
Geometry

3. 7-1 Ratio
A ratio is a comparison of two numbers with the same units by division.
The ratio of 2 to 5 can be expressed three different ways;
2 to 5
2:5
2/5

4. Slope is a ratio, too
Slope formula

5. Ex. 1 Write a ratio expressing the slope of AB.

6. Ratios A ratio can involve more than 2 numbers.
Ex. 2) The ratio of the side lengths of a triangle is 4:7:5 and its perimeter is 96 cm. What is the length of the shortest side?

7. Cross Product Property of Proportions
In a proportion, the product of the extremes(ad) is equal to the product of the means(bc).
If , then ad = bc.

8. Ex. 3 Solve each proportion.

9. Ratio’s (cont’d)
Basically, a ratio has to be a comparison of only like labels (in., ft., yd., & mile)
Referring to our previous example, then 2 ft to 5 ft we can write as a ratio, 2:5.
If we had 3 ft. to 7 in., then we would have to change feet to inches first. 3 • 12 = ___
__ in. to 7 in. OR ___/7 36

10. Converting Ratios
Ratios with different units, convert to same units first. Then simplify the fraction just like you would normally.
Example 1
a) b)

11. Ex. 2 Find slope

12. Using Ratios
Example 2 -The perimeter of the isosceles triangle shown is 56 in. The ratio of LM:MN is 5:4. Find the lengths of the sides and the base of the triangle.

13. Using extended ratios
Example 3 – The measures of the sides in a triangle are in the extended ratio 4:7:5 & its perimeter is 96 cm. What is the length of the shortest side?

14. Application
Ex. 4) Marla is making a scale drawing of her bedroom. Her rectangular room is 12 ½ feet wide and 15 feet long. On the scale drawing, the width of the room is 5 inches. What is the length?

15. Assignment

16. Ex. 4
The ratio of the measures of angles is 5:12:19. What is the measure of the largest angle?

17. Example 1- Solving Proportions
a) b)

18. Example 2

19. Example 3

20. Example 4
A photo of a building has the measurements given in the sketch below. The actual building is 26¼ ft wide. How tall is it?
What is the height of the door in the actual building?

21. Reciprocal Property
If two ratios are equal, then their reciprocals are also equal.
If then