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Chapter 5

Chapter 5 . Group Test. 1. Write an indirect proof that an obtuse triangle does not have a right angle. Given: RST is an obtuse triangle. Prove: RST does not have a right angle.

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Chapter 5

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  1. Chapter 5 Group Test

  2. 1. Write an indirect proof that an obtuse triangle does not have a right angle. Given:RST is an obtuse triangle. Prove:RST does not have a right angle. Let S be an obtuse angle. Assume RST has a right angle. Let R be a right angle. Use direct reasoning to lead to a contradiction. Complete the proof. Def of obtuse Substitution mT < 0 However, by the Protractor Postulate, a triangle cannot have an angle with a measure less than 00. The assumption that has a right angle is false. Therefore, RST does not have a right angle.

  3. 18.7 12.3 2. Find the measures BC and AC. AC = AX + XC = 12.3 + 12.3 = 24.6 BC = 18.7

  4. 3. The diagram shows the approximate distances from Houston to Dallas and from Austin to Dallas. What is the range of distances, d, from Austin to Houston? 240 < 200 + d and d < 240 + 200 240 - 200 < d and d < 240 + 200 240 – 200 < d < 240 + 200 40 < d < 440

  5. 4. Given that bisects and WZ = 7.93, ZY = 8.47, find WX. 8.47 7.93 8.47 7.93 WX = 7.93

  6. y – 3 = (x – ) 5. Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints A(-2, 2) and B(5. 4). y – y1 = m(x – x1)

  7. 6. Given ABC with AB = 6, BC = 7, and CA = 8, find the length of midsegment . X is the midpoint of A XY = ½ BC XY = ½ 7 XY = 7/2 = 3.5 X Y B 7 C

  8. 7. Write the sides of IJK in order from shortest to longest. 65 63 + 52 + J = 180 115 + J = 180 J = 65

  9. 7. Tell whether a triangle can have sides with lengths 7, 5, and 8. 7 + 5 > 8 12 > 8 8 + 5 > 7 13 > 7 7 + 8 > 5 15 > 5 YES

  10. 9. Compare mABC with mCBD. mABC> mCBD

  11. 10. Danny and Dana start hiking from the same base camp and head in opposite directions. Danny walks 6 miles due west, then changes direction and walks for 5 miles to point C. Dana hikes 6 miles due east, then changes direction and walks for 5 miles to point S. Use the diagram to find which hiker is farther from the base camp. Danny Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle and the included angles are not congruent, then the longer third side is across from the larger included angle

  12. 11. What is the value of x, in inches?

  13. 12. In ABC, mADC > mBDC, AC = 3x + 32, and BC = 7x + 16. Find the range of values for x. _____< x <_____ 3x + 32 > 7x + 16 7x + 16 3x + 32 32 > 4x + 16 16 > 4x 4 > x 7x + 16 > 0 Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle and the included angles are not congruent, then the longer third side is across from the larger included angle 7x > -16

  14. 13. Find the value of x. Express your answer in simplest radical form. 720 90 8 4 2 10 9 2 2 2 5 3 3

  15. 14. Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain. Yes, it’s a Pythagorean triple

  16. 15. Tell if the measures 9, 10, and 9 can be side lengths of a triangle. If so, classify the triangle as acute, right, or obtuse.

  17. 16. Find the value of x. Express your answer in simplest radical form.

  18. 17. The Yield sign has a shape of an equilateral triangle with side length of 36 inches. What is the height of the sign? Will a rectangular metal sheet of 36 x 32 inches be big enough to make one sign? 36 18 18 60 60 h 36 36 30 36 Yes, it will be big enough! 32

  19. 18. Find the value of n in the triangle.

  20. 19. If in the right triangle below, what is the value of b?

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