University:
Felician University
Course:
MATH-231 | Geometry I
Academic year:

2023
Views:

207

Pages:

2
Author:

SpaceCadet101

Practice Similarity in Right Triangles Identify the following in right ΔQRS. the hypotenuse: QR the segments of the hypotenuse: QT and TR the altitude: ST the segment of the hypotenuse adjacent to leg QS: QT Write a similarity statement relating the three triangles in the diagram. 1 1. slideshowes.com slideshowes.com ΔABC ~ ΔDBA ~ ΔDAC ΔNOP ~ ΔOQP ~ ΔNQO ΔJKL ~ ΔIMK ~ ΔKML ΔDEF ~ ΔHDF ~ ΔHED ΔXYZ ~ ΔXZA ~ ΔZYX ΔGHI ~ ΔXGI ~ ΔXHG Algebra Find the geometric mean of each pair of numbers. 9 and 4: 6 14 and 6: 2√21 9 and 30: 3√30 25 and 49: 35 4 and 120: 4√30 9 and 18: 9√2 16 and 64: 32 5 and 25: 5√5 12 and 16: 8√3 Use the figure at the right to complete each proportion. q/y = y/t t/q = q/x r/s = s/x x/q = q/y r/y = y/t s/r = r/x Practice (continued) Similarity in Right Triangles Algebra Solve for the value of the variables in each right triangle. 26. 1 27. 9 6 y 2 V10: 3V 10 4V3; 23 29. 6 30. 14 28. 10 25 31. 8 y Z 12 Form G 2V30; 2/21 12 3 65; 35; 6 The diagram shows the parts of a right triangle with an altitude to the hypotenuse. For the two given measures, find the other four. Use simplest radical form. 32. 12, h₁=4 h₂=8; a = 42;143; (24/6 34. (₁=6V3, h₂=3 h₁=9; h₁=9;a=3V3; a=33; 2 26; = 6; h = 12 2 10; 45; 65 h h2 a 12 h₁=4; h = 13;213; (2313 33. a6, h₂9 35. h₁=5,251 a = 215; h₂ = 12; h = 17; (₁ = 85 36. The altitude of the hypotenuse of a right triangle divides the hypotenuse into 45 in. and 5 in. segments. What is the length of the altitude? 15 in. 37. Error Analysis A classmate writes an incorrect proportion to find x. Explain and correct the error. The value of x is the geometric mean of the adjacent segment of the hypotenuse, 3, and the entire hypotenuse, 3+5, or 8. So the correct proportion is 5 3 X 38. Draw a Diagram The sides of a right triangle measure 6V3 in., 6 in., and 12 in. If an altitude is drawn from the right angle to the hypotenuse, what is the length of the segment of the hypotenuse adjacent to the shorter leg? What is the length of the altitude? 3; 3V3 12 in 6 in 9 in 3in 63 in.