Geometry

Today:• 7.1 Instruction• 7.1 Practice

The beginning is the most important part of the work.

Plato

7.1 Solving Problems in Geometry with Ratio and

ProportionObjectives:

1. Find and simplify ratios2. Find and solve proportions3. Find the geometric mean of two

numbers4. Use proportions in real life

Vocabulary:

ratio, proportion, means, extremes

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.

You solved problems by writing and solving equations.

• Write ratios.

• Write and solve proportions.

VocabularyRatio: comparison of two quantities.

Ratio of a and b:

ba or a to b or a : b

Because a ratio is a quotient (division problem), the denominator cannot be zero

Vocabulary

Proportion – an equation of two equal ratios

a

b

c

d

Extremes

Means

8.1

Properties of Proportions

Cross Product Property The product of the extremes equals the product of the means.

a

b

c

d

Extremes

Means

a d b c8.1

Are the following equations proportions?

a) 3 15 4 20

b) 4 12

6 16 c) 2 12

3 18

3•20 = 4•15

60 = 60

YES

4•16 = 6•12

64 = 72

NO

Solving proportions.

a) 2

, solve for x7 21

x

b) 15 3 , solve for y

y 2 y

X = 6

y = ½

c) 3 2 , solve for z

4

z

z

z = -8

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?

Real Life

8.1

2.5’2.5’

Long vs TallModel ____ ____Actual

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 miles43.75 miles

Real Life

8.1

Using Ratios

P = 56 cm

JK:KL is 4:3

Find the length and the width.

J K

M L

8.1

16cm and 12cm

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

N M20in:20in:16in

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

Using Ratios

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 inThe mast of your uncles fishing boat is 30 ft tall. How tall should the mast be on the model?

h = 6.8 in8.2

A. 30, 50, 70

B. 36, 60, 84

C. 45, 60, 75

D. 54, 90, 126

The ratios of the angles in ΔABC is 3:5:7. Find the measure of the angles.

A. 324 students

B. 344 students

C. 405 students

D. 486 students

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.

Geometry

Assignment:• 7.1 p 465 #29,

34, 37, 42, 44, 47-50

• Quiz 7.1-7.3 Friday

The beginning is the most important part of the work.

Plato