7 5 Using Proportional Relationships

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7.5-Using Proportional Relationships

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seven.5-Using Proportional Relationships

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1. 7.five-Using Proportional Relationships 2/five/13

2. Bell Work Convert each measurement. one.6 ft 3 in. to inches 2. v k 38 cm to centimeters Discover the perimeter and area of each polygon. 3. square with side length 13 cm 4. rectangle with length 5.8 m and width ii.5 thousand 75 in. 538 cm P = 52 cm, A =169 cm2 P =16.6 m, A = 14.v m2

3. Helpful Hint Whenever dimensions are given in both feet and inches, you must convert them to either feet or inches before doing whatsoever calculations. Definition one Indirect measurementis any method that uses formulas, like figures, and/or proportions to mensurate an object. The post-obit example shows one indirect measurement technique.

4. Case i Tyler wants to find the height of a telephone pole. He measured the pole'southward shadow and his own shadow and so made a diagram. What is the top h of the pole? AB = 7 ft eight in. = (7  12) in. + 8 in. = 92 in. BC = 5 ft 9 in. = (5  12) in. + 9 in. = 69 in. FG = 38 ft 4 in. = (38  12) in. + 4 in. = 460 in. Pace ane Catechumen the measurements to inches.

5. Ex. 1 continued Step 2 Detect similar triangles. Because the sun's rays are parallel, A F. Therefore ∆ABC ~ ∆FGH by AA ~. Step 3 Notice h. Corr. sides are proportional. Substitute 69 for BC, h for GH, 92 for AB, and 460 for FG. Cantankerous Products Prop. 92h = 69  460 h = 345 Divide both sides by 92. The acme h of the pole is 345 inches, or 28 anxiety 9 inches.

6. Example ii A student who is v ft 6 in. tall measured shadows to notice the height LM of a flagpole. What is LM? Step 1 Convert the measurements to inches. GH = five ft 6 in. = (v  12) in. + 6 in. = 66 in. JH = v ft = (5  12) in. = lx in. NM = xiv ft 2 in. = (14  12) in. + two in. = 170 in.

7. Ex. two connected Step two Notice similar triangles. Because the dominicus's rays are parallel, Fifty Chiliad. Therefore ∆JGH ~ ∆NLM by AA ~. Step 3 Discover h. Corr. sides are proportional. Substitute 66 for BC, h for LM, 60 for JH, and 170 for MN. Cross Products Prop. 60(h) = 66  170 h = 187 Divide both sides by lx. The tiptop of the flagpole is 187 in., or 15 ft. 7 in.

8. Remember! A proportion may compare measurements that accept unlike units. Definition two A calibration drawingrepresents an object every bit smaller than or larger than its actual size. The drawing's scaleis the ratio of any length in the cartoon to the corresponding actual length. For example, on a map with a scale of ane cm : 1500 one thousand, ane centimeter on the map represents 1500 m in actual distance.

9. Example 3 On a Wisconsin road map, Kristin measured a distance of 11 in. from Madison to Wausau. The calibration of this map is 1inch:13 miles. What is the bodily distance between Madison and Wausau to the nearest mile? To observe the bodily altitude x write a proportion comparing the map distance to the actual altitude. Cross Products Prop. Simplify. 10 145 The actual distance is 145 miles, to the nearest mile.

10. Example four Find the actual altitude between City Hall and El Centro College. To find the actual distance x write a proportion comparison the map distance to the actual distance. 1x= 3(300) Cross Products Prop. x 900 Simplify.

11. 9.half-dozen cm v.5 cm Example 5 Lady Liberty holds a tablet in her left hand. The tablet is 7.19 thousand long and iv.14 thousand broad. If you fabricated a calibration drawing using the calibration i cm:0.75 g, what would exist the dimensions to the nearest tenth? Ready proportions to discover the length land width w of the scale drawing. 0.75w = four.14 w  5.5 cm

12. iii.7 in. 3 in. Example 6 The rectangular primal chamber of the Lincoln Memorial is 74 ft long and lx ft wide. Make a scale drawing of the flooring of the bedroom using a scale of i in.:twenty ft. Set proportions to find the length land width w of the scale drawing. 20w = 60 w = iii in

13. Dominion for Similar Triangles & Theorem 1

14. Example 7: using ratios to find perimeters and areas Given that ∆LMN:∆QRS, find the perimeter P and area A of ∆QRS. The similarity ratio of ∆LMN to ∆QRS is By the Proportional Perimeters and Areas Theorem, the ratio of the triangles' perimeters is as well , and the ratio of the triangles' areas is

15. Example 7 continued Perimeter Surface area 13P = 36(ix.1) 132A = (9.1)two(60) P = 25.2 A = 29.4 cm2 The perimeter of ∆QRS is 25.2 cm, and the expanse is 29.iv cm2.

16. Example 8 ∆ABC ~ ∆DEF, BC = 4 mm, and EF = 12 mm. If P = 42 mm and A = 96 mm2 for ∆DEF, find the perimeter and area of ∆ABC. Perimeter Area 12P = 42(4) 122A = (4)2(96) P = xiv mm The perimeter of ∆ABC is xiv mm, and the area is 10.7 mm2.

7 5 Using Proportional Relationships,

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