Geometry Semester 1 Mid Term Review #2

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1 eometry Semester 1 Mid Term Review #2 Multiple Choice Identify the choice that best completes the statement or answers the question. Refer to Figure 1. n H K A D B C m J 1. Name a point NOT contained in lines m, n, or p. a. A c. H b. K d. D F p 2. Name the plane containing lines m and p. f. n h. H g. FC j. JDB 3. Name a point NOT contained in or. a. K c. H b. A d. D 4. Name three points that are collinear. f. B,, F h. J,, F g. C, D, H j. J, D, H A J D B C F. Are points A, C, D, and F coplanar? Explain. D a. Yes; they all lie on plane P. b. No; they are not on the same line. c. Yes; they all lie on the same face of the pyramid. d. No; three lie on the same face of the pyramid and the fourth does not. P A H B C F Find the measurement of the segment. 6. mm, mm. PS =? f mm h. 32. mm g..1 mm j mm P R S 7. Find the value of the variable and H if H is between and I. a. b = 1.2, H = 6.8 c. b = 3, H = 9 b. b = 1.22, H = 7.11 d. b = 3, H = 16

2 y Use the Distance Formula to find the distance between each pair of points. 8. f. h. 6 g. j. 4 W ( 1, 4) T (4, 1) x 1 Find the coordinates of the midpoint of a segment having the given endpoints In the figure, and are opposite rays. and bisects. J 10. What bisects? f. P h. g. j. P 1 2 K If and, what is? a. 13 c. 27 b. 33 d. 12 N M L 12. If and, what is? f. 108 h. 4 g. 14 j If and, what is? a..7 c. 12 b. 41 d Use the figure to find the angles. 14. Name two acute vertical angles. f. h. g. j. H I J 1 2 Q M 1. Name a pair of obtuse adjacent angles. L K 16. Name a linear pair. f. h. g. j. 17. Name an angle supplementary to.

3 18. The measures of two complementary angles are and. Find the measures of the angles. f. 42, 48 h. 8.7 g. 4.2 j. 96, 84 Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular a. pentagon, convex, regular c. hexagon, convex, regular b. hexagon, concave, regular d. hexagon, convex, irregular f. dodecagon, concave, irregular h. decagon, concave, irregular g. dodecagon, convex, irregular j. decagon, convex, regular Find the length of each side of the polygon for the given perimeter. 21. ft. Find the length of each side. 3 s + 2 s s + a. 41 ft, 41 ft, 17 ft, 17 ft, 24 ft c. 0 ft, 0 ft, 20 ft, 20 ft, 30 ft b. 29 ft, 29 ft, 13 ft, 13 ft, 16 ft d. 33. ft, 33. ft, 14. ft, 14. ft, 19 ft Find the circumference of the figure. 22. f. about h. about g. about j. about 3.8 in. Find the area of the figure. 23. a c b..4 d cm 3.1cm 24. Name the bases of the prism. f. UWY and VXZ h. UVZY and UVXW g. UVZY and WXZY j. UVXW and WXZY U V X Z W Y

4 Find the surface area of the solid. 2. Find the volume of the solid. 26. f. 30 h. 84 g. 72 j. 36 Determine whether the conjecture is true or false. ive a counterexample for any false conjecture iven: a concave polygon Conjecture: It can be regular or irregular. a. False; to be concave the angles cannot be congruent. b. True c. False; all concave polygons are regular. d. False; a concave polygon has an odd number of sides. 28. iven: Point B is in the interior of. Conjecture: f. False; may be obtuse. g. True h. False; just because it is in the interior does not mean it is on the bisecting line. j. False;. 29. iven: Two angles are supplementary. Conjecture: They are both acute angles. a. False; either both are right or they are adjacent. b. True c. False; either both are right or one is obtuse. d. False; they must be vertical angles. 30. iven: is supplementary to and is supplementary to. Conjecture: is supplementary to. f. False; they could be right angles. g. False; they could be congruent angles. h. True j. False; they could be vertical angles. Use the following statements to write a compound statement for the conjunction or disjunction. Then find its truth value. p: An isosceles triangle has two congruent sides. q: A right angle measures 90º r: Four points are always coplanar. s: A decagon has 12 sides. 31. q or r a. A right angle measures 90º and four points are always coplanar; false. b. A right angle measures 90º or a decagon has 12 sides; true. c. A right angle measures 90º or four points are always coplanar; true. d. A right angle measures 90º or four points are always coplanar; false.

5 f. A right angle measures 90º or four points are always coplanar, and a decagon has 12 sides; false. g. A right angle measures 90º and four points are always coplanar, or a decagon has 12 sides; false. h. A right angle measures 90º and four points are always coplanar, or a decagon has 12 sides; true. j. A right angle measures 90º or four points are always coplanar, and a decagon has 12 sides; true. a. A decagon has 12 sides and an isosceles triangle has two congruent sides; false. b. A decagon has 12 sides and an isosceles triangle has two congruent sides; true. c. A decagon has 12 sides or an isosceles triangle has two congruent sides; true. d. A decagon has 12 sides or an isosceles triangle has two congruent sides; false. Write the converse of the conditional statement. Determine whether the converse is true or false. If it is false, find a counterexample. 34. If you have a dog, then you are a pet owner. f. If you are a pet owner, then you have a dog. True g. A dog owner owns a pet. True h. If you are a pet owner, then you have a dog. False; you could own a hamster. j. If you have a dog, then you are a pet owner. True Write the inverse of the conditional statement. Determine whether the inverse is true or false. If it is false, find a counterexample. 3. People who live in Texas live in the United States. a. People who do not live in the United States do not live in Texas. True b. People who do not live in Texas do not live in the United States. False; they could live in Oklahoma. c. People who live in the United States live in Texas. False; they could live in Oklahoma. d. People who do not live in Texas live in the United States. True Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample. 36. Two angles measuring 180 are supplementary. f. Two angles not measuring 180 are supplementary. True g. More than two angles measuring 180 are non-supplementary. True h. Non-supplementary angles are not two angles measuring 180. True j. Non-supplementary angles are two angles measuring 180. False; supplementary angles must measure 180. Determine whether statement (3) follows from statements (1) and (2) by the Law of Detachment or the Law of Syllogism. If it does, state which law was used. If it does not, write invalid. 37. (1) She is a girl. (2) Her name is Chris. (3) Chris is a girl's name. a. invalid b. yes; Law of Syllogism c. yes; Law of Detachment

6 38. (1) You are in ninth grade. (2) People who are in ninth grade floss their teeth regularly. (3) You floss your teeth regularly. f. yes; Law of Syllogism g. invalid h. yes; Law of Detachment 39. Find the area of the figure. Round to the nearest tenth if necessary. a. 39 c b d m 9.1 m 40. Find the area of the figure. Round to the nearest tenth if necessary. 16 yd f. 160 h. 180 g. 360 j yd 20 yd 41. Find the area of the figure. Round to the nearest tenth if necessary. a. 66 c. 32 b d m 14 m 14 m 19 m 42. Find the area of a circle having a circumference of. Round to the nearest tenth. Use 3.14 for pi. f units 2 h units 2 g units 2 j units 2 Find the area of the figure. Round to the nearest tenth if necessary a. 148 units 2 c. 130 units 2 b. 140 units 2 d. 122 units 2 Find the lateral area of each prism. Round to the nearest tenth if necessary The dimension labeled 10 is the height of the prism. f. 120 units 2 h. 180 units 2 g. 160 units 2 j. 220 units

7 Find the lateral area of each prism. Round to the nearest tenth if necessary. 4. a units 2 c units 2 b. 10. units 2 d units Find the lateral area of a cylinder with the given measurements. Use 3.14 for pi and round your answer to the nearest tenth. 46. height: 6 yards diameter: 10 yards f h g j Find the surface area of the regular pyramid. Round to the nearest tenth if necessary. 47. a c b d ft Find the volume of the pyramid. Round to the nearest tenth if necessary. 11 ft 48. f. 11,20 m 3 h m 3 g. 14,400 m 3 j m 3 20 m 24 m 30 m 49. Find the volume of a sphere that has a radius of 9. meters. Use 3.14 for. Round to the nearest tenth. a m 3 c m 3 b m 3 d m 3

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