LESSON 7 1 Ratios and Proportions FiveMinute Check

LESSON 7– 1 Ratios and Proportions

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

Over Chapter 6 Complete the statement about parallelogram LMNO. ? A. B. C. D.

Over Chapter 6 Complete the statement about parallelogram LMNO. ? A. B. C. D.

Over Chapter 6 Complete the statement about parallelogram LMNO. OLM ____ ? A. MNO B. LON C. MPN D. MPL

Over Chapter 6 Complete the statement about parallelogram LMNO. ? A. B. C. D.

Over Chapter 6 Find the measure of each interior angle. A. 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

Over Chapter 6 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.

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 nonproportional dimensional change. Mathematical Processes G. 1(A), G. 1(C)

You solved problems by writing and solving equations. • Write ratios. • Write and solve proportions.

• ratio • extended ratios • proportion • extremes • means • cross products

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 1850. 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.

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

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. 5 or 5: 12 is equivalent to ______ 5 x Just as the ratio ___ or 12 12 x 5 x: 12 x, the extended ratio 5: 12: 13 can be written as 5 x: 12 x: 13 x. Write and solve an equation to find the value of x.

Use Extended Ratios 5 x + 12 x + 13 x = 180 30 x = 180 x =6 Triangle Sum Theorem Combine like terms. 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.

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

Use Cross Products to Solve Proportions A. Original proportion Cross Products Property Multiply. y = 27. 3 Answer: y = 27. 3 Divide each side by 6.

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

A. A. b = 0. 65 B. b = 4. 5 C. b = – 14. 5 D. b = 147

B. A. n = 9 B. n = 8. 9 C. n = 3 D. n = 1. 8

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.

Use Proportions to Make Predictions 18 ● 870 = 30 x 15, 660 = 30 x 522 = x ← Students who have a pet ← total number of students Cross Products Property Simplify. 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.

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

LESSON 7– 1 Ratios and Proportions