Warm-ups - Chapter 5 01/12 page 168 #3-8 all (CE)

Section 7-1 Ratio & Proportion

ratio quotient proportion The _______ of one number to another number is the __________ when the 1st number is divided by the second number. A ____________ is an equation stating that two ratios are equal. For example, 𝑎 𝑏 = 𝑐 𝑑 and a:b = c:d are equivalent forms of the same proportion. Either form can be read “a is to b as c is to d.” The number a is called the first term of the proportion. The numbers b, c, and d are the second, third, and fourth terms, respectively. quotient proportion

Extremes: ______________________________ Means: _________________________________ Means – Extremes Property: _____________________________________________________________ first and last terms middle terms the product of the extremes equals the product of the means

Examples: 1. The ratio of 6 to 18 is _____ = _____. 2 Examples: 1. The ratio of 6 to 18 is _____ = _____. 2. The ratio of 30 to 24 is _____ = _____. 3. The extended ratio 10 : 5 : 60 = __________. 6 18 1 3 30 24 5 4 2 : 1 : 12

4. Find the following ratios. a. AD to BC _________________ b 4. Find the following ratios. a. AD to BC _________________ b. mA to mD _________________ c. mD to mC _________________ 10x to 8 → 5x to 4 50 to 130 → 5 to 13 130 to 90 → 13 to 9

5. A poster is 1 m long and 52 cm wide 5. A poster is 1 m long and 52 cm wide. Find the ratio of the width to the length.   6. A mirror is 2 ft wide and 34 in long. Find the ratio of the width to the length. 52 𝑐𝑚 1 𝑚 = 52 𝑐𝑚 100 𝑐𝑚 = 13 𝑐𝑚 25 𝑐𝑚 2 𝑓𝑡 34 𝑖𝑛 = 24 𝑖𝑛 34 𝑖𝑛 = 12 𝑖𝑛 17 𝑖𝑛

7. 1 2 = 𝑥 16 8. 3 5 = 12 𝑥 9. 𝑥 10 = 10 25 2x = 16 3x = 60 25x = 100 x = 20 x = 4 x = 8

10. The measures of 3 angles of a triangle are in the ratio of 2 : 2 : 5. Find the measure of each angle. 11. The measures of 3 angles of a triangle are in the ratio of 3 : 4 : 11. Find the measure of each angle. 2x + 2x + 5x = 180 9x = 180 x = 20 40°, 40°, 100° 3x + 4x + 11x = 180 18x = 180 x = 10 30°, 40°, 110°

12. The ratio of 2 complementary angles is 1 : 2. Find the angles. 13 12. The ratio of 2 complementary angles is 1 : 2. Find the angles. 13. The ratio of 2 supplementary angles is 2 : 7. Find the angles. x + 2x = 90 3x = 90 30° and 60° x = 30 2x + 7x = 180 9x = 180 x = 20 40° and 140°

14. The measures of the angles of a quadrilateral are in the ratio of 7 : 8 : 9 : 12. Find the angles. (n – 2) 180 7x + 8x + 9x + 12x = 360 36x = 360 x = 10 70°, 80°, 90° and 120°

In the figure, 𝐴𝐷 𝐷𝐵 = 𝐶𝐸 𝐸𝐵. 15 In the figure, 𝐴𝐷 𝐷𝐵 = 𝐶𝐸 𝐸𝐵 . 15. If CE = 2, EB = 6, and AD = 3, then DB = _____. 16. If AB = 10, DB = 8, and CB = 7.5, then EB = ____. 2 10 9 3 𝐷𝐵 = 2 6 2DB = 18 8 DB = 9 x 6 7.5 – x 2x = 60 – 8x 7.5 2 8 = 7.5−𝑥 𝑥 10x = 60 x = 6

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