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Geometry The beginning is the most important part of the work. Plato
Today: 7.1 Instruction 7.1 Practice
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7.1 Solving Problems in Geometry with Ratio and Proportion
Objectives: Find and simplify ratios Find and solve proportions Find the geometric mean of two numbers Use proportions in real life Vocabulary: ratio, proportion, means, extremes
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Mathematical Practices 7 Look for and make use of structure.
Content Standards G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). Mathematical Practices 7 Look for and make use of structure. 8 Look for and express regularity in repeated reasoning. CCSS
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You solved problems by writing and solving equations.
Write ratios. Write and solve proportions. Then/Now
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Vocabulary or a to b or a : b Ratio: comparison of two quantities.
Ratio of a and b: or a to b or a : b Because a ratio is a quotient (division problem), the denominator cannot be zero
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Vocabulary Proportion – an equation of two equal ratios Means Extremes
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Properties of Proportions
Cross Product Property The product of the extremes equals the product of the means. Means Extremes 8.1
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Are the following equations proportions?
b) c) 3•20 = 4•15 4•16 = 6•12 60 = 60 64 = 72 YES NO
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Solving proportions. a) X = 6 b) y = ½ c) z = -8
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Real Life A scale model of a car is 20 inches long and 5 inches tall. The actual car is 10 feet long. What is the height of the actual car? Long vs Tall Model ____ ____ Actual 2.5’ 8.1
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Real Life A map has a scale ratio of 2” : 25 miles. If the distance between to cities is 3.5” on the map, how far is it in real life? 43.75 miles 8.1
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Using Ratios P = 56 cm JK:KL is 4:3 Find the length and the width. J K
16cm and 12cm M L 8.1
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Using Ratios The perimeter of an isosceles triangle shown is 56 inches. The ratio of LM : MN is 5 : 4. Find the lengths of the sides and the base of the triangle. L M N 20in:20in:16in
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Using Ratios The perimeter of a triangle is 45in and the ratio of side is 1:3:5. Find the length of each side. 5, 15, 25 in In a triangle, angles are in the ratio of 3:4:8. Find each angle. 36°, 48°, 96° 8.1
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You are building a scale model of your uncles’ fishing boat
You are building a scale model of your uncles’ fishing boat. The boat is 62 ft long and 23 ft wide. The model will be 14 in long. How wide should it be? h = 5.2 in The mast of your uncles fishing boat is 30 ft tall. How tall should the mast be on the model? h = 6.8 in 8.2
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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
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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
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Geometry Assignment: 7.1 p 465 #29, 34, 37, 42, 44, 47-50 Quiz Friday The beginning is the most important part of the work. Plato
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