# Points, Lines, Planes, & Angles - Content.sandbox-njctl

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Points, Lines, Planes, & AnglesPoints & Lines: CLASSWORK1. Name three collinear points on line q and on line s2. Name 4 sets of non-collinear points3. Name the opposite rays on line q and on line s4. How many points are marked on line q?5. How many points are there on line q?Points & Lines: HOMEWORK6. Name three collinear points on line o7. Name 4 sets of collinear points8. Name two opposite rays on line j with endpoint R9. Which 4 points are collinear? What line are they on?10. How many points are there on line j?Points & Lines: CLASSWORKName a point that is collinear with the given points11. O and S12. P and R13. U and T14. U and S15. Name 3 points non-collinear with T and VPoints & Lines: HOMEWORK16. Q and S17. T and R18. U and V19. P and S20. Name 3 points non-collinear with T and UGeometry-PLPA 1 NJCTL.org

Planes: CLASSWORK21. Name a point that is coplanar with A, E, and J22. Name a point that is coplanar with A, C, and I23. Name all the points that are noncoplanar with A, C, and D24. Name all the points that are noncoplanar with F, H, and E25. Where do plane ACH and plane IDC intersect?26. Where do planes ACH, AFJ, and ACD intersect?Planes: HOMEWORK27. Name a point that is coplanar with E, D, and I28. Name a point that is coplanar with A, E, and J29. Name all the points that are noncoplanar with A, F, and H30. Name all the points that are noncoplanar with A, F, and D31. Where do plane JED and plane FHI intersect?32. Where so planes AED, CHI, and JED intersect?Congruence, Distance & Length: CLASSWORK33. Find the distance between point K and point M34. Find the distance between point P and point L35. Find the distance between point O and Point N36. Find the distance between point L and point NCongruence, Distance & Length: HOMEWORK37. Find the distance between point N and point K38. Find the distance between point Q and point L39. Find the distance between point L and point P40. Find the distance between point K and point QGeometry-PLPA 2 NJCTL.org

Congruence, Distance & Length: CLASSWORK41. Given: RV 24SU 8RS ST TURS ?43. Given: RV 37RS TUUV 9ST UV 15ST ?RS ?SU ?42. Given: RV 24SU 8RS ST TUUV ?44. Given: RV 25RT 6RS ST TUUV 3x 1x ?45. Points F, X, and D are collinear, with F between X and D. Draw a diagram and solve for X, if2x 13, FD 7x-6, and XD 2x 70.46. P, A, and Z are collinear. Z is between P and A. Draw a diagram and solve for x, given:ZP 6x-13, ZA 9x 27, and AP 3x 74.47. A, B, and C are collinear with A between B and C. Draw a diagram and solve for x, given:AC 17x – 69, AB 6x 23, and BC 25x-50.Geometry-PLPA 3 NJCTL.orgFX

Congruence, Distance & Length: HOMEWORK48. RV 36TV 12ST TU UVUV ?50. RV 29ST UVRS 7RS ST 1649. RV 36TV 12ST TU UVRS ?51. RV 27SU 6ST TU UVRS ?, RU ?ST ?RS ?RT ?52. D, V, and U are collinear with U between D and V. Draw a diagram and solve for x, given:DU 4x 5, VU 3x-8, and VD 10x-30.53. P, R, and F are collinear with F between R and P. Draw a diagram and solve for x, given: FR 7x-8,FP 4x 20, and PR 13x – 6.54. W, S, and X are collinear with W between X and S. Draw a diagram and solve for x, given: XW 3x 5,SW 7x-18, and XS 6x 19.Constructions & Loci: CLASSWORK55. Draw a circle for each given radius length in the figures below.a)Geometry-PLPAb) 4 NJCTL.org

56. Construct congruent segments for each segment given below. Hint: remember to draw a longer line inany direction to start constructing your congruent segment.a)b)Constructions & Loci: HOMEWORK57. Draw a circle for each given radius length in the figures below.a)b)58. Construct congruent segments for each segment given below. Hint: remember to draw a longer linein any direction to start constructing your congruent segment.a)Geometry-PLPAb) 5 NJCTL.org

Angle Addition Postulate: CLASSWORK – For #59-63, find the missing angle measure.59.#10660. etry-PLPA 6 NJCTL.org

Angle Addition Postulate: HOMEWORK – For #67-71, find the missing angle measure.67.68.69.70.72.71.73.74.Geometry-PLPA 7 NJCTL.org

Angles – Special Angle Pairs: CLASSWORK75. True/False Complementary angles form a right angle76. True/False: Supplementary angles form a straight angle77. Two angles are complementary. One of the angles is 17 , what is the measure of the other angle?78. Two angles are supplementary. One of the angles is 97 , what is the measure of the other angle?79. Two angles are supplementary. One of the angles is three times the size of the other, what is themeasure of the larger angle?80. An angle x is 20 more than its complement. What is the angle’s measure?81. An angle x is 66 less than its complement. What is the angle’s measure?82. An angle x is 46 more than its supplement. What is the angle’s measure?83. An angle x is 18 less than its supplement. What is the angle’s measure?Angles – Special Angle Pairs: HOMEWORK84. True/False: Supplementary angles always sum to 90 85. True/False: Complementary angles sometimes form straight angles86. Two angles are complementary. One of the angles is 57 , what is the measure of the other angle?87. Two angles are supplementary. One of the angles is 43 , what is the measure of the other angle?88. Two angles are supplementary. One of the angles is five times the smaller angle, what is the measureof the larger angle?89. An angle is 74 more than its complement. What is the angle’s measure?90. An angle is 36 less than its complement. What is the angle’s measure?91. An angle is 88 more than its supplement. What is the angle’s measure?92. An angle is 16 less than its supplement. What is the angle’s measure?Geometry-PLPA 8 NJCTL.org

Angles – Proofs of Special Angles: CLASSWORKFind the measures of the missing angles.93.94.Find the value of the variables.95.96.97.98.99.100.Geometry-PLPA 9 NJCTL.org

Angles – Proofs of Special Angles: HOMEWORKFind the measures of the missing angles.101.102.33 45 6Find the value of x.103.104.105.106.107.108.Geometry-PLPA 10 NJCTL.org

Angles – Angle Bisector: CLASSWORKGiven that ray BD bisects ABC in the figure below, find the missing measurements. Note: the questionsare NOT related.Given that ray JL bisects IJK in the figure below, find the value of x.113.114.115.Geometry-PLPA116. 11 NJCTL.org

Angles – Angle Bisector: HOMEWORKGiven that ray RT bisects QRS in the figure below, find the missing measurements. Note: the questionsare NOT related.RQSTGiven that ray JL bisects IJK in the figure below, find the value of x.121.122.123.Geometry-PLPA124. 12 NJCTL.org

Angles – Locus & Angle Constructions: CLASSWORK125. Construct a congruent angle for each figure below.a)ABCb)DEFAngles – Locus & Angle Constructions: HOMEWORK126. Construct a congruent angle for each figure below.a)HGIb)KJLGeometry-PLPA 13 NJCTL.org

Angles –Angle Bisectors & Constructions: CLASSWORK127. Construct the angle bisector of each angle below using any construction method of your choice.a)b)Angles –Angle Bisectors & Constructions: HOMEWORK128. Construct the angle bisector of each angle below using any construction method of your choice.a)b)Geometry-PLPA 14 NJCTL.org

Points, Lines, Planes and AngleReview Multiple Choice129.Intersecting lines are non-coplanara.alwaysb.sometimesc.never130.Two non-parallel lines intersect at one point.a.alwaysb.sometimesc.never131.Two points are collinear.a.alwaysb.sometimesc.never132.Three points are collinear.a.alwaysb.sometimesc.never133.Three points are coplanar.a.alwaysb.sometimesc.never134.Four points are coplanar.a.alwaysb.sometimesc.never135.When two planes intersect, they do so:a.at a pointb.along a linec.along a plane136.All points along a line are collinear.a.alwaysb.sometimesc.never137.Opposite rays (circle all that apply):a.are collinearb.have the same endpointc.sometimes overlapd.form a straight angleGeometry-PLPA 15 NJCTL.org

138.If points A, B, C are collinear with C between A and B, the segment addition postulate is:a.AB BC ACb.BA CB ACc.BC CA ABd.BC AC CA139.Points J, K and L are collinear with J between L and K. If KJ 2x - 3, LK 9x 7 and LJ 4x - 8,solve for x:a.6b.-6c.-4d.4140.Two rays that have a common endpoint could form (check all that apply):a. an angleb. a straight linec. opposite raysd. a vertex141.Acute angles are:a. less than 90⁰b. greater than 90⁰ but less than 180⁰c. equal to 180⁰d. greater than 180⁰ but less than 360⁰142.Obtuse angles are:a. less than 90⁰b. greater than 90⁰ but less than 180⁰c. equal to 180⁰d. greater than 180⁰ but less than 360⁰143.Adjacent angles (circle all that apply):a. have a common sideb. sum to 90⁰c. share a common vertexd. are less than 90⁰144.Complementary angles (circle all that apply):a. sum to 90⁰b. sum to 180⁰c. form a straight angled. form a right anglee. are adjacent anglesGeometry-PLPA 16 NJCTL.org

145.Supplementary angles (circle all that apply):a. sum to 90⁰b. sum to 180⁰c. form a straight angled. form a right anglee. are adjacent angles146.An angle is 34⁰ more than its compliment. What is the measure of the angle?a. 64⁰b. 124⁰c. 28⁰d. 62⁰147.An angle is 58⁰ less than its supplement. What is the measure of the angle?a. 33⁰b. 61⁰c. 123⁰d. 154⁰148.Find the measures of the angles to the right.a.b.c.d.1 113 2 3149.Find the value of x in the figure to the right.a. ½b. 9(x 19) c. 12d. 24(5x 17) 150.An angle bisector (circle all that apply):a. forms two congruent anglesb. is a line or a rayc. is equidistant from the sides of the angled. forms two adjacent angles151.The statement, "the whole is the sum of the parts" refers to (circle all that apply):a. complementary anglesb. the segment addition postulatec. adjacent anglesd. the angle addition postulateGeometry-PLPA 17 NJCTL.org

Points, Lines, Planes and AnglesReview Constructed Response152. Points B, D, F, H and J are collinear and are in the following order D is between J and B F is between D and J B is between F and H JH 47, FB 12, FD DB BH and JF 3x - 7Draw a diagram of the points, solve for x and solve for JF.153.An angle is 36⁰ less than its complement. What is the measure of the angle?154. An angle is 102⁰ more than its supplement. What is the measure of the angle?155. If F is in the interior of APB and m APB (5x 11)⁰, m APF (6x - 6)⁰ and m FPB (9x - 23)⁰: Draw a diagram Solve for x What is the m APF and m APB?Geometry-PLPA 18 NJCTL.org

Answer Key1. KLI & HLJ2. HLK, HLI, KLJ, ILJ3. LK, LI, LJ, LH4. 35. Infinite6. VRS7. QVW, TUR, QUS, VRS8. RW, RU9. TURW, j10. Infinite11. Q12. Q13. R14. P15. PSOU or R16. O17. U18. O19. U20. POSQ or V21. F22. J23. FHJI24. ACJI25. CH26. A27. J28. F29. EDJI30. CHEJ31. JI32. D33. 534. 1235. 436. 337. 638. 1439. 1240. 1741. 442. 1243. ST 6 RS 11 SU 1744. 545. 9Geometry-PLPA46. 547. 248. 649. 1850. ST 9 RS 7 RT 1651. RS 18 RU 2452. 953. 954. 855. Check Constructions56. Check Constructions57. Check Constructions58. Check Constructions59. 26⁰60. 72⁰61. 23⁰62. 123⁰63. 193⁰64. 1565. 366. 367. 71⁰68. 14⁰69. 17⁰70. 57⁰71. 33⁰72. 5.8666.73. 274. 775. True76. True77. 73⁰78. 83⁰79. 135⁰80. 55⁰81. 12⁰82. 113⁰83. 81⁰84. False85. False86. 33⁰87. 137⁰88. 150⁰89. 82⁰ 19 90. 27⁰91. 134⁰92. 82⁰93. 63o, 117o, 63o94. 128o, 128o, 52o95. x 1796. x 797. x 1698. x 1399. x 16 & y 6100.x 4&y 6101.126o, 54o, 54o102.147o, 147o, 33o103.x 11104.x 7105.x 13106.x 10107.x 20 & y 5108.x 10 & y 20109.39o, 39o110.44o, 44o111.112o, 56o112.46o, 92o113.x 24114.x 6115.x 10116.x 9117.48o, 96o118.88o, 176o119.83o, 83o120.53o, 53o121.x 10122.x 21123.x 8124.x .CheckConstructions128.CheckConstructionsNJCTL.org

Review Answer Key Multiple Choice129. C130. A131. A132. B133. A134. B135. B136. A137. A, B, D138. C139. B140. A, B, C, D141. A142. B143. A, C144. A, D145. B, C146. D147. B148. C149. D150. A, B, C, D151. B, DGeometry-PLPAReview Answer Key Constructed Response152.x 12 JF 29153.x 27⁰154.x 141⁰155. 20 NJCTL.org

Points, Lines, Planes, & Angles Points & Lines: CLASSWORK 1. Name three collinear points on line q and on line s 2. Name 4 sets of non-collinear points 3. Name the opposite rays on line q and on line s 4. How many points are marked on line q? 5. How many points are there on line q? Points & Lines: HOMEWORK 6.

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