Name: Date: School: Facilitator: 7.06 Proportions and Similar Triangles Use the diagram to fill in the blanks. 1. ? = 2. Determine the length of each segment. Show all work for full credit. 3. = Show your work below 4. = Show your work below ? = Name: Date: School: Facilitator: 7.07 Special Triangle Segments Find the value of the variable given the triangles are similar. Answer the additional questions. Show all work. Name the property you used in your problem. J 1. a = What type of segment is WX? Which property did you use? Show your work in the yellow area below. 3. x = What type of segment is AD? What type of segment is HJ? Which property did you use? Show your work in the yellow area below. 2. x = What type of segment is AD? What type of segment is HJ? Which property did you use? Show your work in the yellow area below. Name: Date: School: Facilitator: 8.01 Altitudes 1. Find the geometric mean between 4 and 25. Show your work. = x = 2. Find the geometric mean between 4 and = . Show your work. x = Find the value of h, x, and y in the following problems. 3. Find h h = 4. John and Carol have both set up a proportion to solve for x in the diagram below. John : x 11 3 x Who is correct? Then solve for x. Who is correct? x = 5. Find x and h. x = h = Carol: 3 x x 8 Name: School: Date: Facilitator: 8.02 Pythagorean Theorem Show all work. Some blanks have been provided to help you. You must show work, then make the proper selection or you will not receive credit. In each right triangle, find the missing side length to the nearest tenth. Select the correct answer. 1. a = , b = , c = a + b = c + = + = x = 17.0 2. a = , b = , c = 22.9 25.0 31.0 a + b = c + = + = x = 6.0 10.4 12.0 13.4 Select the correct answer. 3. The legs of a right triangle are 5 and 13. Find the length of the hypotenuse to the nearest tenth. a = , b = , c = a + b = c + = + = x = 8.6 10.0 12.0 13.9 18.0 4. The screen of a 32-inch high definition television has a diagonal length of 31.5 inches. If the TV screen is 27.5 inches wide, find the height of screen to the nearest tenth of an inch. a = , b = , c = a + b = c + = + = x = 4.0 inches 15.4 inches 16.0 inches 5.The sides of a triangle are 4, 5 and 6. Is it a right triangle? a = , b = , c = a + b = c + = + = = Is it a right triangle? yes no 6. The sides of a triangle are 15, 20 and 25. Is it a right triangle? a = , b = , c = a + b = c + = + = = Is it a right triangle? yes no 41.8 inches Name: Date: School: Facilitator: 7.06 Proportions and Similar Triangles Use the diagram to fill in the blanks. 1. ? = FG 2. Determine the length of each segment. Show all work for full credit. 3. =9 Show your work below AC/BC=AF/GF (6+4)/6=(GF+6)/GF 10GF=6GF+36 10GF-6GF=36 4GF=36 GF=36/4 GF=9 4. =6 Show your work below AE/FE=AD/CD (FE+15)/FE=14/4 4FE+60=14FE 14FE-4FE=60 10FE=60 FE=60/10=6 ? = CE Name: School: Date: Facilitator: 8.02 Pythagorean Theorem Show all work. Some blanks have been provided to help you. You must show work, then make the proper selection or you will not receive credit. In each right triangle, find the missing side length to the nearest tenth. Select the correct answer. 1. a = 24, b = 7, c = X a + b = c 24 +7 = X 576 +49 = 625 x = 25 17.0 2. a = X, b = 6, c = 12 22.9 X=25.0 25.0 31.0 a + b = c X +6 = 12 X +36 = 144 x = 10.4 6.0 X=10.4 10.4 12.0 13.4 Select the correct answer. 3. The legs of a right triangle are 5 and 13. Find the length of the hypotenuse to the nearest tenth. a = 5, b = 13, c = x a + b = c 5 +13 = x 25 +169 = x x = 13.9 8.6 10.0 12.0 x=13.9 13.9 18.0 4. The screen of a 32-inch high definition television has a diagonal length of 31.5 inches. If the TV screen is 27.5 inches wide, find the height of screen to the nearest tenth of an inch. a = x, b = 27.5, c = 31.5 a + b = c x +27.5 = 31.5 x +756.25 = 992.25 x = 15.4 4.0 inches x=15.4 15.4 inches 16.0 inches 5.The sides of a triangle are 4, 5 and 6. Is it a right triangle? a = 4, b = 5, c = 6 a + b = c 4 +5 = 6 16 +25 = 36 41 = 36 Is it a right triangle? yes No no 6. The sides of a triangle are 15, 20 and 25. Is it a right triangle? a = 15, b = 20, c = 25 a + b = c 15 +20 = 25 225 +400 = 625 625 = 625 Is it a right triangle? YES yes no 41.8 inches Name: Date: School: Facilitator: 7.07 Special Triangle Segments Find the value of the variable given the triangles are similar. Answer the additional questions. Show all work. Name the property you used in your problem. J 1. a = 2 What type of segment is WX? Angle bisector Which property did you use? Line WX is is equidistant from the sides of the angle when measured along a segment perpendicular to the sides of the angle. Show your work in the yellow area below. Angle WXY=angle WXZ 3. x = 20 What type of segment is AD? Median What type of segment is HJ? Median 2. x = 8 What type of segment is AD? Altitude What type of segment is HJ? Altitude Which property did you use? Show your work in the yellow area below. HJ/AD=HI/AC HJ=4(12/6) =4*2 =8 Which property did you use? Joins vertex of triangle to the midpoint of opposite side Show your work in the yellow area below. BD=DC GJ=JI GJ/BD=JI/DC Name: Date: School: Facilitator: 8.01 Altitudes 1. Find the geometric mean between 4 and 25. Show your work. 4 X = X 25 x = 10 2. Find the geometric mean between 4 and 4 x = . Show your work. X x=1 Find the value of h, x, and y in the following problems. 3. Find h h = 4. John and Carol have both set up a proportion to solve for x in the diagram below. John : x 11 3 x Who is correct? Then solve for x. Who is correct? ?John x = 5.745 5. Find x and h. x=3 h = 5.196 Carol: 3 x x 8