1. Ratios and Proportions
LESSON 7–1
Ratios and Proportions

2. Five-Minute Check (over Chapter 6) TEKS Then/Now New Vocabulary
Example 1: Real-World Example: Write and Simplify Ratios
Example 2: Use Extended Ratios
Key Concept: Cross Products Property
Example 3: Use Cross Products to Solve Proportions
Example 4: Real-World Example: Use Proportions to Make Predictions
Key Concept: Equivalent Proportions
Lesson Menu

3. Complete the statement about parallelogram LMNO.?
Complete the statement about parallelogram LMNO. A. B. C. D.
5-Minute Check 1

4. Complete the statement about parallelogram LMNO.? A. B. C. D.
5-Minute Check 2

5. Complete the statement about parallelogram LMNO. OLM  ____?
A. MNO
B. LON
C. MPN
D. MPL
5-Minute Check 3

6. Complete the statement about parallelogram LMNO.? A. B. C. D.
5-Minute Check 4

7. Find the measure of each interior angle.
mA = 60, mB = 120, mC = 60, mD = 120
B. mA = 65, mB = 115, mC = 65, mD = 115
C. mA = 65, mB = 115, mC = 60, mD = 120
D. mA = 70, mB = 110, mC = 70, mD = 110
5-Minute Check 5

8. Which of the statements about an isosceles trapezoid is false?
A. The diagonals are congruent.
B. Two sides are both congruent and parallel.
C. Two pairs of base angles are congruent.
D. One pair of sides are congruent.
5-Minute Check 6

9. Mathematical Processes G.1(A), G.1(C)
Targeted TEKS
Preparation for G.10(B) Determine and describe how changes in the linear dimensions of a shape affect its perimeter, area,
surface area, or volume, including proportional and non-proportional dimensional change.
Mathematical Processes
G.1(A), G.1(C)
TEKS

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

11. ratio extended ratios proportion extremes means cross products
Vocabulary

12. Answer: The athlete-to-student ratio is 0.3.
Write and Simplify Ratios
SCHOOL The number of students who participate in sports programs at Central High School is 520. The total number of students in the school is 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.
0.3 can be written as
Answer: The athlete-to-student ratio is 0.3.
Example 1

13. The country with the longest school year is China, with 251 days
The country with the longest school year is China, with 251 days. Find the ratio of school days to total days in a year for China to the nearest tenth. (Use 365 as the number of days in a year.)
A. 0.3
B. 0.5
C. 0.7
D. 0.8
Example 1

14. Use Extended Ratios
In ΔEFG, the ratio of the measures of the angles is 5:12:13, and the perimeter is 90 centimeters. Find the measures of the angles.
Just as the ratio or 5:12 is equivalent to or 5x:12x, the extended ratio 5:12:13 can be written as 5x:12x:13x. Write and solve an equation to find the value of x.
___ 5 12
______ 5x
12x
Example 2

15. 5x + 12x + 13x = 180 Triangle Sum Theorem
Use Extended Ratios
5x + 12x + 13x = 180 Triangle Sum Theorem
30x = 180 Combine like terms.
x = 6 Divide each side by 30.
Answer: So, the measures of the angles are 5(6) or 30, 12(6) or 72, and 13(6) or 78.
Example 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. Concept

18. Cross Products Property
Use Cross Products to Solve Proportions A.
Original proportion
Cross Products Property
Multiply.
y = 27.3
Divide each side by 6.
Answer: y = 27.3
Example 3

19. Cross Products Property
Use Cross Products to Solve Proportions B.
Original proportion
Cross Products Property
Simplify.
Add 30 to each side.
Divide each side by 24.
Answer: x = –2
Example 3

20. A.
A. b = 0.65
B. b = 4.5
C. b = –14.5
D. b = 147
Example 3

21. B.
A. n = 9
B. n = 8.9
C. n = 3
D. n = 1.8
Example 3

22. Use Proportions to Make Predictions
PETS Monique randomly surveyed 30 students from her class and found that 18 had a dog or a cat for a pet. If there are 870 students in Monique’s school, predict the total number of students with a dog or a cat.
Write and solve a proportion that compares the number of students who have a pet to the number of students in the school.
Example 4

23. ← Students who have a pet ← total number of students
Use Proportions to Make Predictions
← Students who have a pet
← total number of students
18 ● 870 = 30x Cross Products Property
15,660 = 30x Simplify.
522 = x Divide each side by 30.
Answer: Based on Monique's survey, about 522 students at her school have a dog or a cat for a pet.
Example 4

24. 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

25. Concept

26. Ratios and Proportions
LESSON 7–1
Ratios and Proportions