NJCTL



Points, Lines, Planes, & AnglesPoints & Lines: CLASSWORKName three collinear points on line q and on line sName 4 sets of non-collinear pointsName the opposite rays on line q and on line sHow many points are marked on line q?How many points are there on line q?Points & Lines: HOMEWORKName three collinear points on line oName 4 sets of collinear pointsName two opposite rays on line j with endpoint RWhich 4 points are collinear? What line are they on?How many points are there on line j?Points & Lines: CLASSWORKName a point that is collinear with the given pointsO and SP and RU and TU and SName 3 points non-collinear with T and VPoints & Lines: HOMEWORKQ and ST and RU and VP and S Name 3 points non-collinear with T and UPlanes: CLASSWORKName a point that is coplanar with A, E, and JName a point that is coplanar with A, C, and IName all the points that are noncoplanar with A, C, and DName all the points that are noncoplanar with F, H, and EWhere do plane ACH and plane IDC intersect?Where do planes ACH, AFJ, and ACD intersect?Planes: HOMEWORKName a point that is coplanar with E, D, and IName a point that is coplanar with A, E, and JName all the points that are noncoplanar with A, F, and HName all the points that are noncoplanar with A, F, and DWhere do plane JED and plane FHI intersect?Where so planes AED, CHI, and JED intersect?Congruence, Distance & Length: CLASSWORKFind the distance between point K and point MFind the distance between point P and point LFind the distance between point O and Point NFind the distance between point L and point NCongruence, Distance & Length: HOMEWORKFind the distance between point N and point KFind the distance between point Q and point LFind the distance between point L and point PFind the distance between point K and point QCongruence, Distance & Length: CLASSWORKGiven: RV = 24 SU = 8 RS = ST = TURS = ?Given: RV = 24 SU = 8 RS = ST = TUUV = ?Given: RV = 37 RS = TU UV = 9 ST + UV = 15ST = ?RS = ?SU = ?Given: RV = 25 RT = 6 RS = ST = TU UV = 3x +1x = ?Points F, X, and D are collinear, with F between X and D. Draw a diagram and solve for X, if FX = 2x+13, FD = 7x-6, and XD = 2x+70.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.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.Congruence, Distance & Length: HOMEWORKRV = 3650. RV = 29TV = 12 ST = UVST = ?ST = TU = UV RS = 7RS = ?UV = ? RS + ST = 16RT = ? RV = 3651. RV = 27TV = 12 SU = 6ST = TU = UV ST = TU = UVRS = ? RS = ?, RU = ?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)b) 56. Construct congruent segments for each segment given below. Hint: remember to draw a longer line in any 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 line in any direction to start constructing your congruent segment. a)b) Angle Addition Postulate: CLASSWORK – For #59-63, find the missing angle measure.65.64.66.63.62.61.60.59.Angle Addition Postulate: HOMEWORK – For #67-71, find the missing angle measure.74.73.70.71.69.68.67.72.Angles – Special Angle Pairs: CLASSWORK 75. True/FalseComplementary angles form a right angle 76. True/False: Supplementary angles form a straight angle 77. 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 the measure 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: HOMEWORK 84. True/False: Supplementary angles always sum to 90° 85. True/False: Complementary angles sometimes form straight angles 86. 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 measure of 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?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. Angles – Proofs of Special Angles: HOMEWORKFind the measures of the missing angles.101. 102. Find the value of x.103. 104. 105. 106. 107. 108. Angles – Angle Bisector: CLASSWORKGiven that ray BD bisects ∠ ABC in the figure below, find the missing measurements. Note: the questions are NOT related.Given that ray JL bisects ∠ IJK in the figure below, find the value of x.113. 114. 115. 116. Angles – Angle Bisector: HOMEWORK Given that ray RT bisects ∠ QRS in the figure below, find the missing measurements. Note: the questions are NOT related. Given that ray JL bisects ∠ IJK in the figure below, find the value of x.121.122. 123. 124. Angles – Locus & Angle Constructions: CLASSWORK 125. Construct a congruent angle for each figure below. a) b) Angles – Locus & Angle Constructions: HOMEWORK 126. Construct a congruent angle for each figure below. a) b)Angles –Angle Bisectors & Constructions: CLASSWORK 127. Construct the angle bisector of each angle below using any construction method of your choice. a)b) Angles –Angle Bisectors & Constructions: HOMEWORK 128. Construct the angle bisector of each angle below using any construction method of your choice. a)b) Points, Lines, Planes and AngleReview Multiple ChoiceIntersecting lines are _________________ non-coplanaralwayssometimesneverTwo non-parallel lines _________________ intersect at one point.alwayssometimesneverTwo points are _________________ collinear.alwayssometimesneverThree points are _________________ collinear.alwayssometimesneverThree points are _________________ coplanar.alwayssometimesneverFour points are _________________ coplanar.alwayssometimesneverWhen two planes intersect, they do so: at a pointalong a linealong a planeAll points along a line are _________________ collinear.alwayssometimesneverOpposite rays (circle all that apply):are collinearhave the same endpointsometimes overlapform a straight angleIf points A, B, C are collinear with C between A and B, the segment addition postulate is:AB + BC = ACBA + CB = ACBC + CA = ABBC + AC = CAPoints 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:6-6-44Two rays that have a common endpoint could form (check all that apply):an anglea straight lineopposite raysa vertexAcute angles are:less than 90?greater than 90? but less than 180?equal to 180?greater than 180? but less than 360?Obtuse angles are:less than 90?greater than 90? but less than 180?equal to 180?greater than 180? but less than 360?Adjacent angles (circle all that apply):have a common sidesum to 90?share a common vertexare less than 90?Complementary angles (circle all that apply):sum to 90?sum to 180?form a straight angleform a right angleare adjacent anglesSupplementary angles (circle all that apply):sum to 90?sum to 180?form a straight angleform a right angleare adjacent anglesAn angle is 34? more than its compliment. What is the measure of the angle?64?124?28?62?An angle is 58? less than its supplement. What is the measure of the angle?33?61?123?154?Find the measures of the angles to the right. Find the value of x in the figure to the right. ? 9 12 24An angle bisector (circle all that apply):forms two congruent anglesis a line or a rayis equidistant from the sides of the angleforms two adjacent anglesThe statement, "the whole is the sum of the parts" refers to (circle all that apply):complementary anglesthe segment addition postulateadjacent anglesthe angle addition postulatePoints, Lines, Planes and AnglesReview Constructed Response Points B, D, F, H and J are collinear and are in the following orderD is between J and BF is between D and JB is between F and HJH = 47, FB = 12, FD = DB = BH and JF = 3x - 7 Draw a diagram of the points, solve for x and solve for JF.An angle is 36? less than its complement. What is the measure of the angle? An angle is 102? more than its supplement. What is the measure of the angle? If F is in the interior of ∠APB and m∠APB = (5x +11)?, m∠APF = (6x - 6)? and m∠FPB = (9x +- 23)?:Draw a diagram Solve for xWhat is the m∠APF and m∠APB?Answer KeyKLI & HLJHLK, HLI, KLJ, ILJLK, LI, LJ, LH3InfiniteVRSQVW, TUR, QUS, VRSRW, RUTURW, jInfiniteQQRPPSOU or ROUOUPOSQ or VFJFHJIACJICHAJFEDJICHEJJID512436141217412ST=6 RS=11 SU=175952618ST = 9 RS = 7 RT = 16RS = 18 RU = 24998Check ConstructionsCheck ConstructionsCheck ConstructionsCheck Constructions26? 72? 23? 123? 193? 15 3 3 71? 14? 17? 57? 33? 5.8666... 2 7 True True 73? 83? 135? 55? 12? 113? 81? False False 33? 137? 150? 82? 27? 134?82?63o, 117o, 63o 128o, 128o, 52o x = 17 x = 7 x = 16 x = 13 x = 16 & y = 6 x = 4 & y = 6 126o, 54o, 54o 147o, 147o, 33o x = 11 x = 7 x = 13 x = 10 x = 20 & y = 5 x = 10 & y = 20 39o, 39o 44o, 44o 112o, 56o 46o, 92o x = 24 x = 6 x = 10 x = 948o, 96o 88o, 176o 83o, 83o 53o, 53o x = 10 x = 21 x = 8 x = 4.5Check ConstructionsCheck ConstructionsCheck ConstructionsCheck ConstructionsReview Answer Key Multiple ChoiceCAABABBAA, B, DCBA, B, C, DABA, CA, DB, CDBCDA, B, C, DB, DReview Answer Key Constructed Response x = 12 JF = 29x = 27?x = 141?m∠APF = 18?m∠APB = 31? ................
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