1. Geometry The beginning is the most important part of the work. Plato
Today:
7.1 Instruction
7.1 Practice

2. 7.1 Solving Problems in Geometry with Ratio and Proportion
Objectives:
Find and simplify ratios
Find and solve proportions
Find the geometric mean of two numbers
Use proportions in real life
Vocabulary:
ratio, proportion, means, extremes

3. Mathematical Practices 7 Look for and make use of structure.
Content Standards
G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
Mathematical Practices
7 Look for and make use of structure.
8 Look for and express regularity in repeated reasoning.
CCSS

4. You solved problems by writing and solving equations.
Write ratios.
Write and solve proportions.
Then/Now

5. Vocabulary or a to b or a : b Ratio: comparison of two quantities.
Ratio of a and b:
or a to b or a : b
Because a ratio is a quotient (division problem),
the denominator cannot be zero

6. Vocabulary Proportion – an equation of two equal ratios Means Extremes
8.1

7. Properties of Proportions
Cross Product Property The product of the extremes equals the product of the means.
Means
Extremes
8.1

8. Are the following equations proportions?b) c)
3•20 = 4•15
4•16 = 6•12
60 = 60
64 = 72
YES NO

9. Solving proportions. a)
X = 6 b)
y = ½ c)
z = -8

10. Real Life
A scale model of a car is 20 inches long and 5 inches tall. The actual car is 10 feet long. What is the height of the actual car?
Long vs Tall
Model ____ ____
Actual
2.5’
8.1

11. Real Life
A map has a scale ratio of 2” : 25 miles. If the distance between to cities is 3.5” on the map, how far is it in real life?
43.75 miles
8.1

12. Using Ratios P = 56 cm JK:KL is 4:3 Find the length and the width. J K
16cm and 12cm M L
8.1

13. Using Ratios
The perimeter of an isosceles triangle shown is 56 inches. The ratio of LM : MN is 5 : 4. Find the lengths of the sides and the base of the triangle. L M N
20in:20in:16in

14. Using Ratios
The perimeter of a triangle is 45in and the ratio of side is 1:3:5. Find the length of each side.
5, 15, 25 in
In a triangle, angles are in the ratio of 3:4:8. Find each angle.
36°, 48°, 96°
8.1

15. You are building a scale model of your uncles’ fishing boat
You are building a scale model of your uncles’ fishing boat. The boat is 62 ft long and 23 ft wide. The model will be 14 in long. How wide should it be?
h = 5.2 in
The mast of your uncles fishing boat is 30 ft tall. How tall should the mast be on the model?
h = 6.8 in
8.2

16. The ratios of the angles in ΔABC is 3:5:7
The ratios of the angles in ΔABC is 3:5:7. Find the measure of the angles.
A. 30, 50, 70
B. 36, 60, 84
C. 45, 60, 75
D. 54, 90, 126
Example 2

17. Brittany randomly surveyed 50 students and found that 20 had a part-time job. If there are 810 students in Brittany's school, predict the total number of students with a part-time job.
A. 324 students
B. 344 students
C. 405 students
D. 486 students
Example 4

18. Geometry
Assignment:
7.1 p 465 #29, 34, 37, 42, 44, 47-50
Quiz Friday
The beginning is the most important part of the work.
Plato