Ch. 5 Review

Name__________________________________________________Period______________Date_______________________________ Chapter 5 Review 1. Name the longest side and the shortest side of each triangle. 2. Name the largest and the smallest angle of each triangle. 3. Is it possible for a triangle to have sides with the lengths indicated? a. 10, 9, 8 b. 6, 6, 20 c. 7, 7, 14.1 d. 16, 11, 5 e. 0.6, 0.5, 1 4. The lengths of two sides of a triangle are given. Write the numbers that best complete the statement: _____< S < _______. a. 6, 9 b. 16, 13 c. 100, 100 d. 37, 25 e. 0.8, 1. 5. m∠T = 3x + 2,m∠U = 4x + 5,and m∠V = 7x − 9 . List the sides of ΔTUV in order from shortest to longest. 6. What is the shortest possible distance between a point and a line? 7. What is the shortest possible distance between a point and a plane? 8. An isosceles triangle has 2 congruent sides 8.3 units long. What is the longest possible base to the first decimal place? 9. D is equidistant from the sides of ∠BAC. Find the value of x. ∠BAD=25° and ∠CAD= (5x+5). 10. Use the sides e, f, g, h, and i to complete: ______<______<_____<_____<_____. 11. In ΔABC, G is the centroid and CD= 12. Find CG and GD. AG=9, find GE. 12. Name the median, altitude, and angle bisector of ΔABC. 13. Lines d, e, and f are perpendicular bisectors of ΔABC and meet at G. If GA=2x+2, GB=2y-‐4, GC=8, and BE=2z-‐6, find x, y, and z. Use the drawing of ΔABC for questions 14 to 16. 14. AD is an angle bisector. m∠DCA=7x+7, m∠CAD=9x-‐11, and m∠ADC=88. Find m∠BAD. 15. AD is an altitude. m∠DBA=8x-‐4 and m∠BAD=5x+3. Find m∠DAB. 16. AD is a median. DC=6 and BD=3x-‐2. Find x. 17. Determine the relationship between the measures of the given angles. a) ∠ABC, ∠BCA b) ∠EAF, ∠FAD c) ∠FEA, ∠DFA 18. Determine the relationship between the lengths of the given sides. a) BC, DE b) AC, AE c) AD, AF Answers: 1. Longest CB, shortest AB, longest DF, shortest EF 2. Largest:∠B, smallest:∠C, largest:∠F, smallest:∠E 3. A)yes B)no C)no D)no E)yes 4. A) 3<S<15 B) 3<S<29 C) 0<S<200 D) 12<S<62 E) 0.2<S<1.8 5. UV<TV<TU 6. A perpendicular line segment. 7. A perpendicular line segment. 8. 16.5 units 9. x=4 10. e<g<h<i<f 11. CG=8, GD=4, GE=4.5 12. Median: CE, altitude: AD, angle bisector: BF 13. X=3, y=6, z=5 14. m∠BAD=43 15. m∠DAB=38 8
x=
3 16.
17. a) ∠ABC > ∠BCA b) ∠EAF > ∠FAD c) ∠FEA < ∠DFA 18. a) BC > DE b) AC > AE c) AD > AF

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