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Example 2. Given A MNP - A HKG, MN = 6 , NP = 4, MP =D8 2022/04/09 13:16 H. k a. Find all the sides of A HKG if the ratio of similarity is 1: 3. b. What are the measures of the other angles of the two triangles if mzP = 30 and mzK = 100? Solution: a. Since the corresponding sides of similar triangles are proportional and the ratio of similarity is 1:3; then MN NP MP 1 AK KG HG 3 6. 4. 8. h Work with the three proportions separately. MN NP MP HR 3\ XG HG %3D 3\ k g = (6)(3) g = 18 Therefore, HK = 18 cm h (4)(3) h = 12 KG = 12 cm k = (8)(3) k = 24 HG = 24 cm b. Since AMNP~AHKG and ZP corresponds to ZG, then ZP G. Therefore, mzG = 30. ZK corresponds to zN, then zK ZN. Therefore, mzN = 100. Since the sum of the interior angles of a triangle is 180, and 4M corresponds to zH, then mzM = mzH = 180 - (mzK + mzG). Therefore, mzM = mzH = 180- (100 + 30) = 50 Tell whether the two triangles are always, sometimes, or never similar. a. Two equilateral triangles. b. Two isosceles triangles. C. A right triangle and an acute triangle. -triangle -l31/3 1/3 II ||

Example 2. Given A MNP - A HKG, MN = 6 , NP = 4, MP =D8 2022/04/09 13:16 H. k a. Find all the sides of A HKG if the ratio of similarity is 1: 3. b. What are the measures of the other angles of the two triangles if mzP = 30 and mzK = 100? Solution: a. Since the corresponding sides of similar triangles are proportional and the ratio of similarity is 1:3; then MN NP MP 1 AK KG HG 3 6. 4. 8. h Work with the three proportions separately. MN NP MP HR 3\ XG HG %3D 3\ k g = (6)(3) g = 18 Therefore, HK = 18 cm h (4)(3) h = 12 KG = 12 cm k = (8)(3) k = 24 HG = 24 cm b. Since AMNP~AHKG and ZP corresponds to ZG, then ZP G. Therefore, mzG = 30. ZK corresponds to zN, then zK ZN. Therefore, mzN = 100. Since the sum of the interior angles of a triangle is 180, and 4M corresponds to zH, then mzM = mzH = 180 - (mzK + mzG). Therefore, mzM = mzH = 180- (100 + 30) = 50 Tell whether the two triangles are always, sometimes, or never similar. a. Two equilateral triangles. b. Two isosceles triangles. C. A right triangle and an acute triangle. -triangle -l31/3 1/3 II ||

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter20: Ratio And Propor Tion
Section: Chapter Questions
Problem 43A: The proportion AB=CDcompares the sides of two triangles like those in Figure 209. Determine the...
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Example 2. Given A MNP -A HKG, MN = 6 , NP = 4, MP = 8 2022/04/09 13:16 8. k a. Find all the sides of A HKG if the ratio of similarity is 1: 3. b. What are the measures of the other angles of the two triangles if mzP = 30 and mzK = 100? Solution: a. Since the corresponding sides of similar triangles are proportional and the ratio of similarity is 1:3; then MN NP MP 1 AK KG HG 3 6. 4 8. Work with the three proportions separately. MN NP MP HR 3. KG HG %3D 3\ k g = (6)(3) g = 18 Therefore, HK = 18 cm h = (4)(3) h = 12 KG = 12 cm k = (8)(3) k = 24 HG = 24 cm b. Since ΔΜΝΡ~ΔHKG and ZP corresponds to ZG, then ZP =4 G. Therefore, mzG = 30. ZK corresponds to ZN, then zK ZN. Therefore, mzN = 100. Since the sum of the interior angles of a triangle is 180, and ZM corresponds to ZH, then 180 - (mzK + mzG). Therefore, mzM = mzH = 180 - (100 + 30) = 50 mzM = mzH Tell whether the two triangles are always, sometimes, or never similar. a. Two equilateral triangles. b. Two isosceles triangles. C. A right triangle and an acute triangle. d. An equilateral triangle and an equiangular triangle. e. Two scalene triangles. f. An isosceles triangle and a scalene triangle. g. A right triangle and a scalene triangle. -31/3 1/3
Transcribed Image Text:Example 2. Given A MNP -A HKG, MN = 6 , NP = 4, MP = 8 2022/04/09 13:16 8. k a. Find all the sides of A HKG if the ratio of similarity is 1: 3. b. What are the measures of the other angles of the two triangles if mzP = 30 and mzK = 100? Solution: a. Since the corresponding sides of similar triangles are proportional and the ratio of similarity is 1:3; then MN NP MP 1 AK KG HG 3 6. 4 8. Work with the three proportions separately. MN NP MP HR 3. KG HG %3D 3\ k g = (6)(3) g = 18 Therefore, HK = 18 cm h = (4)(3) h = 12 KG = 12 cm k = (8)(3) k = 24 HG = 24 cm b. Since ΔΜΝΡ~ΔHKG and ZP corresponds to ZG, then ZP =4 G. Therefore, mzG = 30. ZK corresponds to ZN, then zK ZN. Therefore, mzN = 100. Since the sum of the interior angles of a triangle is 180, and ZM corresponds to ZH, then 180 - (mzK + mzG). Therefore, mzM = mzH = 180 - (100 + 30) = 50 mzM = mzH Tell whether the two triangles are always, sometimes, or never similar. a. Two equilateral triangles. b. Two isosceles triangles. C. A right triangle and an acute triangle. d. An equilateral triangle and an equiangular triangle. e. Two scalene triangles. f. An isosceles triangle and a scalene triangle. g. A right triangle and a scalene triangle. -31/3 1/3
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