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1.2 Points, Lines, and Planes definition- undefined terms- points- line- plane- collinear points- coplanar points- a. Name three points that are collinear. b. Name four points that are coplanar. c. Name three points that are not collinear. Term Line Line segment Definition Symbol Picture Ray Opposite rays endpointsinitial point- GEOMETRIC DRAWING… -Draw 3 noncollinear points J, K, L -Then draw -Then draw -Last draw -Draw the intersection of a plane and a line. -Draw the intersection of two planes. -Draw two points, A and B. Then sketch AB. Add point C on the segment between A and B. ⃗⃗⃗⃗⃗ , ⃡⃗⃗⃗⃗ -Draw points A, B, C, D, E, with no three collinear. Then sketch ̅̅̅̅ 𝐴𝐵 , 𝐵𝐶 𝐶𝐷, ̅̅̅̅ 𝐷𝐸 , ⃗⃗⃗⃗⃗ 𝐴𝐸 Together... 1) The three undefined terms of geometry are ________________________________________. 2) Lines intersect at a ____________________. 3) Planes intersect at a ___________________. 4) How do we represent line AB? _______________ 5) How do we refer to the line segment AB? ______________ 6) Points that lie on the same line are called _______________________. C A D E F 7) Name 2 planes that intersect at line AD. ______________________ 8) Are points C, E, F and A coplanar? ______________________ 9) Name the 4th point that is coplanar with points C, E, and F. _______ 1.3 Segments and Their Measures distance- length- between- The Ruler Postulate A B C D E F G -3 -2 -1 0 1 2 3 Segment Addition Postulate- EX 2 (a) XY= 12 (b) MN=3 EX 3 AB=x BC= x+6 AC=24 Find: YZ=4 XZ= ________ OP= 18 MP=31 NO=_______ B is between A and C x= ______ AB=______ BC= ______ Ex. 4 Q is between T and W TQ=2x+3 TW= 22 QW=x+4 Find: x= ________ TQ= ________ QW= _______ Segment bisectorMidpoint- congruent segments- Sketch the 3 collinear points. Then write the Segment Addition Postulate for the points. e. A is between P and L f. R is between T and G Ex. 5 Q is the midpoint of PR. What are PG, QR, and PR if PQ = 6x – 7 and QR = 5x + 1 In the diagram, AE = 20, BD = 6, and AB = BC = CD. Find each length. j. BC n. CD k. AB o. DE l. CA p. BE m. DA q. CE 1.4 Measuring Angles anglesidevertex- NAMING ANGLES Angles that have the same measure are called . *Lengths are equal. Segments are congruent.* *Measures are equal. Angles are congruent.* Angle Addition Postulate Example: Solve for x. 155° 12 m<1 = 4x-20 m<2 = 3x +14 CLASSIFYING ANGLES acute right obtuse straight Classify the angle. a. m A = 180º c. m C = 90º b. m d. m D = 34º B = 106º Use the diagram to answer the questions. e. Is ABD DBE? f. Is DBA EBC? g. Are DBE and EBC adjacent? h. Are ABD and CBE adjacent? Name the vertex and sides of the angle. Then estimate its measure. 1.5 Angle Pair Relationships Adjacent angles- vertical angles- linear pair- Ex. 1 a) Identify all vertical angles b) Identify all linear pairs c) Identify adjacent angles 1 3 2 4 Vertical angle measures… Linear pair measures… Ex. 2 Angle 5 has a measure of 56º, what are the measures of the other 3 angles? 5 Ex. 3 6 8 7 Solve for x and y. Then give the measures of the four angles. (y + 20) º (3x +5) º (4y – 15) º (x + 15) º Complementary Angles- Supplementary Angles- Ex. 4 Complementary or Supplementary? Adjacent or nonadjacent? a. b. c. d. Ex. 5 Ex. 6 Ex. 7 A is complementary to B, which is supplementary to what are the measures of A and B? D is complementary to E and supplementary to are the measures of the other two angles? C. If m A is 76º, F. If m E is 34º, what Find x and y, and then find the measures of all four angles. (3x + 20) º yº (5x – 50) º Angle bisector- 1.7 Distance and Midpoint Midpoint Formula Find the coordinates of the midpoint. a. (1, 2) and (3, 6) b. (-3, -5) and (-7, 10) The midpoint of AB is C. Use the coordinates of A and C to find the coordinates of B. c. A (3, 4) and C (7,8) d. A(-4,0) and C (0,-2) Find the coordinates of the midpoints. g. B(7,6) M(-5, 4) h. A(0,0) B(-8,6) Find the coordinates of the other endpoints of a segment with the given endpoint and midpoint M. i. D(-2, -4) M(5, -4) j. Q(4,2) M(7,3) Distance Formula- Find the distance between the two points. a. (1, 2) and (4, 6) b. (-2, -3) and (0, 0) Use the distance formula to determine if JK KL h. J (3, -5) i. J (0, -8) K (-1, 2) K (4, 3) L (-5, -5 L (-2, -7) c. (1,-3) and (-4,2)