Geometric - Triangles Inequalities

**Practice** **1. Write the angles of △KLM in order from smallest to largest.** ∠K, ∠L, ∠M **2. Write the sides of △DEF in order from shortest to longest.** DE, EF, DF **3. Tell whether a triangle can have sides with the given lengths. Explain.** a. 8, 3, 10.3: **Yes**, 8 + 3 > 10.3, 3 + 10.3 > 8, 8 + 10.3 > 3 b. 10.5, 18.3, 18.8: **No**, 10.5 + 18.3 is not greater than 18.8 **4. The distance from Kara's school to the theater is 9 km. The distance from her school to the zoo is 16 km. If the three locations form a triangle, what is the range of distances from the theater to the   zoo?** Greater than 7 km and less than 25 km **Inequalities in Two Triangles** **5. Compare PR and SV.** PR > SV **6. Compare m∠KJL and m∠MLK.** m∠KJL < m∠MLK **7. Find the range of values for x.** 3.25 < x < 7 **The Pythagorean Theorem** **8. Find the value of x.** x = √106 **9. Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain.** x = √110, **No**, because √110 is not a whole number. **10. Tell if the side lengths 12, 15, and 16 can be the sides of a triangle. If so, classify the triangle as acute, obtuse, or right.** Yes, it is a right triangle. **11. A landscaper wants to place a stone walkway from one corner of the rectangular lawn to the opposite corner. What will be the length of the walkway? Round to the nearest inch.**   94 ft 4 in **Applying Special Right Triangles** **12. A yield sign is an equilateral triangle with a side length of 36 inches. What is the height of the sign? Round to the nearest inch.** 31 in **Find the values of the variables. Give your answers in simplest radical form.** **13.** x = 8√2 **14.** x = 11√2 **15.** x = 5√3 y = 10 **Find each measure.** 1. m∠B = 62° 2. m∠WXY = 34° 3. BC = 21 4. MQ, NO, and PQ are the perpendicular bisectors of ΔRST. Find RS and RQ. RS = 18, RQ = 18 5. EG and FG are angle bisectors of ΔDEF. Find m∠GEF and the distance from G to DF. m∠GEF = 44°; distance from G to DF = 3.7 6. In ΔXYZ, XC = 2BC and ZW = 1/8 XY. Find XY, XZ, and YZ. XY = 174, XZ = 87, YZ = 177 7. Find the perimeter of ΔJKL with vertices J(-5, 2), K(-5, 10), and L(1, 4). Perimeter = 24 8. In ΔGHP, right angle P, PR = 51, GJ = 140, and m∠GRP ≈ 71°. Find m∠GHP and PR. m∠GHP ≈ 19°, PR ≈ 133 9. Write an indirect proof that two obtuse angles cannot form a linear pair. 10. Write the angles of ΔRBH in order from smallest to largest. ∠H, ∠B, ∠R 11. Write the sides of ΔRTV in order from shortest to longest. RV, RT, TV 12. The distance from Arville to Branton is 114 miles. The distance from Branton to Camford is 247 miles. If the three towns form a triangle, what is the range of distances from Arville to Camford?   133 mi < d < 361 mi 13. Compare m∠ZPV and m∠SPV. m∠ZPV < m∠SPV 14. Find the range of values for x. 2.3 < x < 8.5 15. Find the missing side length in the triangle. Tell if the side lengths form a Pythagorean triple. Explain. 3√15, No, not a whole number 16. Tell if the measures 16, 20, and 27 can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. No 17. An IMAX screen is 62 feet tall and 82 feet wide. What is the length of the screen's diagonal? Round to the nearest inch. 102 ft 10 in **Find the values of the variables. Give your answers in simplest radical form.**   18. x = 8√2 19. x = 10√2 y = 5√3 20. x = 15 y = 15√3 Answers 47. x = 2√10 48. x = 2√33 49. 6; the lengths do not form a Pythagorean triple because 4.5 and 7.5 are not whole numbers. 50. 40; the lengths do form a Pythagorean triple because they are nonzero whole numbers that satisfy the equation   a² + b² = c². 51. not a triangle 52. triangle; obtuse 53. triangle; right 54. triangle; acute 55. x = 6√2 56. x = 2√3 57. x = 32 58. x = 24, y = 24√3 59. x = 6√3, y = 12 60. x = 14√3, y = 12√3 61. 21 ft 3 in 62. 15 ft 7 in