9.3 Start Thinking. 9.3 Warm Up. 9.3 Cumulative Review Warm Up. In the diagram below, CD is an altitude to the hypotenuse of. 1.
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1 9.3 Start Thinking In the diagram below, is an altitude to the hpotenuse of. 1. Prove:. Prove: 3. Use the information from the two proofs to make a conclusion about the two smaller triangles in the diagram. 9.3 Warm Up Given that the triangles are similar, find the missing side length umulative Review Warm Up Use the diagram to find m 1 and m ( 1) 300 Geometr opright ig Ideas Learning, LL Resources b hapter
2 Name ate 9.3 Practice In Eercises 1 and, identif the similar triangles. 1. K. X U J M L Y Z In Eercises 3, find the value of. 3. Y.. Z W 8 X In Eercises 8, find the geometric mean of the two numbers.. 3 and 1 7. and 1 8. and In Eercises 9, find the value of You are designing a diamond-shaped kite. You know that = 38. centimeters, = 7 centimeters, and = 81. centimeters. You want to use a straight crossbar. bout how long should it be? opright ig Ideas Learning, LL Geometr Resources b hapter 301
3 Name ate 9.3 Practice In Eercises 1 3, use the diagram. 1. Identif the similar triangles.. Which segment s length is the geometric mean of and? 3. Find,, and. In Eercises, find the value of In Eercises 7 9, find the geometric mean of the two numbers and 8. 1 and 9. 1 and 0 In Eercises 1, find the value(s) of the variable(s) w z z You build a cornhole game. The game is constructed from a sheet of plwood supported b two boards. The two boards form a right angle and their lengths are 1 inches and. inches. 1 in. in. a. Find the length of the plwood to the nearest inch.. in. b. You put in a support that is altitude to the hpotenuse of the right triangle. What is the length of the support? Round our answer to the nearest tenth. c. Where does the support attach to the plwood? Eplain. 30 Geometr opright ig Ideas Learning, LL Resources b hapter
4 Name ate 9.3 Enrichment and Etension Geometric Mean 1. In right triangle RST, altitude SU is drawn to the hpotenuse RT, RS = 8, and the ratio of RU to UT is 1 to 3. What is the length of RT?. In right triangle, altitude is drawn to hpotenuse. If = and = 1, find the length of,, and. ab 3. The harmonic mean of a and b is. The Greek mathematician Pthagoras a + b found that three equall taut strings on stringed instruments will sound harmonious if the length of the middle string is equal to the harmonic mean of the lengths of the shortest and longest string. a. Find the harmonic mean of and 1. b. Find the harmonic mean of and 1. c. Will equall taut strings whose lengths have the ratio of : : 1 sound harmonious? Eplain our reasoning.. In polgon PQRS at the right, PQ = PS and QR = SR. Find PR and QS. Q In Eercises and, the vertices of are given. Use the point-slope formula to find the coordinates of a point such that is the altitude to the hpotenuse.. ( 1, 1 ), ( 1, 1 ), ( 1, 1). (, 0 ), (, 8 ), (, 8) P R 7. Square in the diagram at the right has side lengths of 1, and the midpoints of its sides are labeled P, Q, R, and S. Find the length of a side of the shaded square. P S S Q R opright ig Ideas Learning, LL Geometr Resources b hapter 303
5 Name ate 9.3 Puzzle Time Wh id The Forest Ranger hange Jobs? E F G H I omplete each eercise. Find the answer in the answer column. Write the word under the answer in the bo containing the eercise letter.. LEF bisector WS geometric HE 9.1 TIME 1. TO WNTE 18.8 FOREST 7.1 OVER 7. EN omplete the sentence.. If the is drawn to the hpotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other.. In a right triangle, the altitude from the right angle to the hpotenuse divides the hpotenuse into two segments. The length of the altitude is the mean of the lengths of the two segments.. Identif the smallest similar triangle using the diagram for. Find. Round our answer to the nearest tenth.. = 3, = 1, = E. = 1, =, = 13 F. = 1, = 8, = 17 Find the geometric mean of the two numbers. Round our answer to the nearest tenth. G. 1 and H. 18 and 30 I. 0 and 3 length THE 3. NEW GRSS altitude EUSE 1. GREENER 3.1 WITH. TURN. TREE Geometr opright ig Ideas Learning, LL Resources b hapter
1. Sample answer: A, B, D. 3. D, E, F 4. plane C 6. C, E 7. E. 8. Sample answer: C ray infinite; zero. 4. no; yes 5.
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