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math422feb262017.notebook Proportions and February 27, 2017 Similar polygons hw Geometry p. 243244 written # 15,192528,30 p. 247 #2,4,6,16 1. In Colombia, $1.00 (US) = 2,894 pesos. If I want to buy something that costs 130,000 pesos, how many dollars is that? 2. If $1.00(US) = .9 Euros, what is 12 Euros worth in US dollars? 3. You are making a recipe for cookies that (among other things) calls for 2/3 cup sugar and 1.5 cups of flour. You realize you only have 1/2 cup sugar, and its late so you can't borrow or buy any. If you want to continue baking, how much flour should you use so that the sugar:flour ratio stays correct? 4. You are in a foreign country and sign up to a 10 km bike ride. How far is that in miles if 1 mile is about 1.6 km? 5. A 6 foot tall person casts a 2 foot shadow, while a nearby flagpole casts a 15 foot shadow at the same time. Can you figure out how tall the flagpole is? math422feb262017.notebook February 27, 2017 Review of Ratio and Proportion The ratio of one number to another is the quotient of the first number divided by the second. Ratios can be written as 2:3 or as the fraction 2/3. ratios are usually expressed in lowest terms For ex., the ratio of geometry books to calculus books on my shelf might be 9:12 or 3:4 or 3/4 A ratio can be thought of as a comparison between two quantities. the ratio of a team's wins to losses a baseball batters ratio of hits to at bats (batting average) the scale on a map , for ex 1 " : 3 miles converting dollars to euros or pesos converting km to miles or vice versa Sometimes we use algebraic expressions to represent ratios. For example if the measures of the angles in a triangle is 2:3:4, then the angles can be represented by 2x, 3x, and 4x, and to find the actual measures of those angles, we would solve 2x+3x+4x=180 A proportion is written when 2 ratios are equal. math422feb262017.notebook February 27, 2017 Properties of Proportions Similar polygons: same shape, different size Two polygons are similar (~) if their vertices can be matched up so that 1)corresponding angles are congruent 2) corresponding sides are proportional math422feb262017.notebook F February 27, 2017 The triangles are similar iF AB=4,DE=6,CB=8 FIND FE E' C A' E A A B D E D T D B R D' B' C' C S F A B I If angle F=72, find the measure of angle B, and the measure of angle I If both polygons are similar parallelograms. R C E D A T If these right triangles are similar, and the measure of angle T=36, AT=24, CA=10, RE=5, find ED, and the measure of angle R math422feb262017.notebook February 27, 2017
