Changes for 2nd Semester:1.Two separate interactive notebooks (Notes & Scholar Work)

2.No intervention/reteach week

3.Retakes will be taken after school on determined dates. All assignments & notes must be complete

4.Crunchymath.weebly.com

Opening Activity

1. A tight end scored 6 touchdowns in 14 games. Find the ratio of touchdowns per game.

2. In a schedule of 6 classes, Marta has 2 elective classes. What is the ratio of elective to non-elective classes in Marta’s schedule.3. An artist in Portland, Oregon, makes bronze sculptures of dogs. The ratio of the height of a sculpture to the actual height of the dog is 2:3. If the height of the sculpture is 14 inches, find the height of the dog.

D. N. A.

94

3 2) x

Solve the following equations.

637 1) x

155

6 3)

a 643

2 4) y

Slides Skills Practice Practice

1, 2, 7, 8, 9 1-5 1-3

11, 12, 13 6-11 4-9

15 12-15 10-12

17 13-15

Geometry Chapter 7: Proportions and Similarity

Chapter 7 Test on Friday 1/18Retake 2/7 or 2/8

Chapter 7-1:

Proportions

• ratio

• proportion

• cross products

• extremes

• means

• Write ratios.

• Use properties of proportions.

Reinforcement of CA Standard 6NS1.3 Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. (Key)

Prerequisite Algebra ReviewSolve the following equation:

94

3 2) x

Multiply both sides by the reciprocal of the fraction.

1

9

4

3x

3

4

3

4

3

36

12

12x

12x

Prerequisite Algebra Review (cont.)

Solve the following equation:

155

6 3)

a

1

15

5

6a

6

5

6

5

2

25a

5

2

Prerequisite Algebra Review (cont.)

Solve the following equation:

643

2 4) y

1

10

3

2y

2

3

2

3

15a

510

3

2y

RatiosA comparison of two quantities using division.

Example: The ratio of 5 and 7 can be written as 5:7 or as the fraction and we say the ratio is “five to seven”. 7

5

a

ba b or :

Example # 2:

• Gary has a bag with 4 marbles, 3 books, 5 pencils, and 2 erasers.

a. What is the ratio of pencils to books?

5:3

b. What is the ratio of marbles to the total number of items in the bag?

4:14 2:7 (Must be reduced!)

Write a Ratio

SCHOOL The total number of students who participate in sports programs at Central High School is 500. The total number of students in the school is 2000. Find the athlete-to-student ratio to the nearest tenth.To find this ratio, divide the number of athletes by the total number of students.

Answer: The athlete-to-student ratio is 1:4.

4:14

1

2000

500

students of # total

athletes of #or

1. A tight end scored 6 touchdowns in 14 games. Find the ratio of touchdowns per game.

2. In a schedule of 6 classes, Marta has 2 elective classes. What is the ratio of elective to non-elective classes in Marta’s schedule.

3. An artist in Portland, Oregon, makes bronze sculptures of dogs. The ratio of the height of a sculpture to the actual height of the dog is 2:3. If the height of the sculpture is 14 inches, find the height of the dog.

Proportions• If two ratios are equal, they can be written

as a proportion.

d

c

b

a

Extremes Means

Proportion Practice

12

8

6

4) a

• Which proportions are not correct?

8

12

4

6) b

6

12

4

8) f

6

12

8

4) c

8

4

12

6) d

8

6

12

4) e

48 = 48 48 = 48 24 96

48 = 48 32 72 48 = 48

Proportion Practice

7

54

xx574

• Solve the following proportions

5

28x

yy

2

2

3

)2(23 yy

423 yy4y Check your answer!

Solve each proportion.

405

2 6)

x

x

21

10

7 7)

6

4

5

20 8)

x

8

35

4

5x 9)

2

7

3

1 10)

x

5

3

3

15 11)

x

Using Ratios Example #1• The Perimeter of a rectangle is 60 cm. The ratio of

AB:BC is 3:2. Find the length and width of the rectangle. A

D C

B

3:2 is in lowest terms.

AB:BC could be 3:2, 6:4, 9:6, 12:8,

etc.

AB = 3x

BC = 2x

Perimeter = l + w+ l + w

60 = 3x + 2x + 3x + 2x

60 = 10x

x = 6

L = 3(6) = 18

W = 2(6) = 12

Find the measures of the sides of each triangle.

12. The ratio of the measures of the sides of a triangle is 3:5:7, and its perimeter is 450 centimeters.

13. The ratio of the measures of the sides of a triangle is 5:6:9, and its perimeter is 220 meters.

14. The ratio of the measures of the sides of a triangle is 4:6:8, and its perimeter is 126 feet.

Find the measures of the angles in each triangle.

15) The ratio of the measures of the angles is 4:5:6.

mA+ mB+ mC = 180o Triangle Sum Thm.

2x + 3x + 4x = 180o

9x = 180o

x = 20o

mA = 40o

mB = 60o

mC = 80o

• The angle measures in ABC are in the extended ratio of 2:3:4. Find the measure of the three angles.

Using Ratios Example #2

A

C

B

2x3x

4x

• The ratio of the measures of the three side lengths of a ABC are , and the perimeter is 19 m. Find the measure of each side of the triangle.

Using Ratios Example #3

51

41

21 ::

1951

41

21 xxx

Change the fractions into common denominators?

19204

205

2010 xxx

Multiply everything by the common denominator. 1920202020 20

4205

2010 xxx

3804510 xxx38019 x20x 4)20(

5)20(

10)20(

51

41

21

In a triangle, the ratio of the measures of three sides is 5:12:13, and the perimeter is 90 centimeters. Find the measure of the shortest side of the triangle.A 13 cm B 15 cm C 38 cm D 39 cm

Extended Ratios in Triangles

The shortest side is 15 centimeters. The answer is B.Check Add the lengths of the sides to make sure that

the perimeter is 90.

A. 10.5 ft

B. 14 ft

C. 17.5 ft

D. 37 ft

In a triangle, the ratio of the measures of three sides is 3:4:5, and the perimeter is 42 feet. Find the measure of the longest side of the triangle.

Proportion Properties(The names are not important, the ideas are!!!)

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

d

c

b

a if bcad then

B.

Answer: –2

Solve Proportions by Using Cross Products

Cross products

Simplify.

Add 30 to each side.

Divide each side by 24.

A. 0.65

B. 4.5

C. –14.5

D. 147

A.

1. A

2. B

3. C

4. D

A. 9

B. 8.9

C. 3

D. 1.8

B.

TRAINS A boxcar on a train has a length of 40 feet and a width of 9 feet. A scale model is made with a length of 16 inches. Find the width of the model.

Solve Problems Using Proportions

Answer: The width of the model is 3.6 inches.

Substitution

Cross products

Multiply.

Divide each side by 40.

Answer: The width of the model is 3.6 inches.

Solve Problems Using Proportions

Substitution

Cross products

Multiply.

Divide each side by 40.

Proportion Practice #2• A picture of a tree is shown, the actual tree

is 84 in. tall. How wide is the tree?

in2

13

in4

11

4

5 widthpic

2

7height pic

x width in tree84height tree

842745

x

x2

7)84(

4

5

x14)84(5 x14420 30x

A. 0.6 m

B. 2.24 m

C. 2.52 m

D. 28.57 m

Two large cylindrical containers are in proportion. The height of the larger container is 25 meters with a diameter of 8 meters. The height of the smaller container is 7 meters. Find the diameter of the smaller container.

HomeworkChapter 8.1

Pg 383:

2 – 9, 12 – 26,56 – 61, 63, 64