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Chapter 1 Student Notes

Chapter 1 Student Notes. Chapter 1 Test Tuesday , August 29 th. 1.1 Points, Lines and Planes. Point - . A B. C D. m. Line - . Collinear - . A B C. T / F A and B are Collinear T / F A and C are Collinear T / F A, B and C are Collinear. Plane - .

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Chapter 1 Student Notes

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  1. Chapter 1 Student Notes Chapter 1 Test Tuesday, August 29th

  2. 1.1 Points, Lines and Planes

  3. Point - A B

  4. C D m Line -

  5. Collinear - A B C • T / F A and B are Collinear • T / F A and C are Collinear • T / F A, B and C are Collinear

  6. Plane - A B C P

  7. Coplanar - A B C D G EF • Name 3 Coplanar Points ________ • Name 3 Noncoplanar Points _________ • T/F C, D and G are coplanar • T/F A, B, E, F are coplanar • T/F A, B, C, E are coplanar

  8. Draw and Label each of the following • n and m intersect at P • p contains N • P contains A and B, but not C

  9. Draw and Label each of the following • 4. mintersects P at X • 5. P and R intersect at m

  10. 1.2Segments Objective: Learn the language of Geometry Become familiar with segments and segment measure

  11. Line Segment - A B

  12. Betweenness of Points - A B C

  13. Measure of aSegment - M 6 N

  14. Segment Congruence - R 7 T S 7 U

  15. Segment Congruence is marked on a figure in the following manner. A 12 12 C B

  16. Multiple Pairs of Congruent Segments A D From the markings on the above figure, make 2 congruence statement. B C

  17. A is between C and D. Find Each Measure. C 4 A 3 D C A 7 D 15 • AC = 4, AD = 3, Find CD = ______ • CD = 15, AD = 7, Find AC = _____

  18. A is between C and D. Find Each Measure. C x + 1 A x + 3 D 3x - 5 • 3. AC = x + 1, AD = x + 3, CD = 3x – 5, Find x = _____

  19. A is between C and D. Find Each Measure. C 8 A 5 D C A 12 D 20 • AC = 8, AD = 5, Find CD = ______ • CD = 20, AD = 12, Find AC = _____

  20. A is between C and D. Find Each Measure. C 2x + 1 A 2x + 3 D 5x – 10 • 3.AC = 2x + 1, AD = 2x + 3, CD = 5x – 10, Find x = ___

  21. A 8 C 4 B D 8 B A D B A C is between A and B in each figure. Select the figure that has AB = 12. Select all that apply. A. C is between A and B. B. B is between A and D. B is between A and D. AB = 2x + 5, BD = 3x + 4, AD = 6x – 3 B is between A and D. AB = 2x + 2, DB = 4x +2, DA =34 D B A Answer: ____________

  22. 1.3Distance and Midpoint

  23. Distance on a Number Line = Use the number line to find the length of each segment. A B C D -5 0 5 AB = BC = AD = BD =

  24. Distance on a Coordinate Plane Distance Formula A(2, 2) B(-4, 1) C(2, -4) Find the length of each segment. AB =

  25. A(2, 2) B(-4, 1) C(2, -4) Find the length of each segment. BC

  26. A B C D -5 0 5 Midpoint on a Number Line Midpoint = Find the midpoint of each segment. 1. AB 2. AD

  27. Find the midpoint of each segment. A B C D -5 0 5 3. BC If A is the midpoint of EC, what is the location for point E?

  28. Midpoint on a Coordinate Plane A(2, 2) B(-4, 1) C(2, -4) Midpoint = ( ) x1 + x2 , y1 + y2 2 2 Find the midpoint of each segment. 1. AB = ( ) = ( )

  29. Midpoint on a Coordinate Plane A(2, 2) B(-4, 1) C(2, -4) Find the midpoint of each segment. 1. BC = ( ) = ( )

  30. Midpoint on a Coordinate Plane A(2, 2) B(-4, 1) C(2, -4) Find the midpoint of each segment. 2.AC = ( ) = ( )

  31. M is the midpoint of AB. Given the following information, find the missing coordinates. M(2, 6) , B(12, 10) , A ( ? , ? ) Midpoint = ( ) x1 + x2 , y1 + y2 2 2

  32. M is the midpoint of AB. Given the following information, find the missing coordinates. M(6, -8) , A(2, 0) , B ( ? , ? ) Midpoint = ( ) x1 + x2 , y1 + y2 2 2

  33. 1.4Angle Measure

  34. Ray - R B A D S E

  35. Angle–

  36. Angles and Points • Points _______________________________ • G ____________________ • H ____________________ • E ____________________ D G H F E

  37. Naming Angles Name the angle at the right as many ways as possible. • ________ • ________ • ________ • ________ D G H F 2 E

  38. Naming Angles • Name the angles at the right as many ways as possible. • _______ • _______ • _______ • _______ • _______ • _______ • _______ • _______ J M L 3 2 K

  39. Naming Angles • Name the angles at the right as many ways as possible. • _________ • _________ • _________ J M L 3 2 There is more than one angle at vertex K, K __________________ ____________________________________ ● ● ● ● ● ●

  40. ________ different types of angles: Types of Angles Right angle: Acute angle:

  41. Types of Angles Obtuse angle: Straight angle: Can also be called __________ ________________.

  42. Congruent Angles 33o W M 33o

  43. Multiple Sets of Congruent Angles A B • __________ • __________ C D

  44. Angle Bisector KM is an angle bisector. What conclusion can you draw about the figure at the right? J M • _________________ • or • ________________ 4 L 6 K

  45. Adding Angles • When you want to add angles, use ______________________ _____________________________________________________________.. • If you add m1 + m2, what is your result? _____________________________. J M 48o ● 28o L ● ● 1 2 K

  46. Angle Addition Postulate The sum of the two smaller angles adjacent angles will _______________________________________________________________________________________________. R U 1 T 2 Complete: m______ + m ______ = m _______ or m______ + m ______ = m _______ S

  47. Example Draw your own diagram and answer this question: If ML is an angle bisector of PMY and mPML = 87, then find: mPMY = _______ mLMY = _______

  48. JK is an angle bisector of LJM. mLJK = 4x + 10, mKJM = 6x – 4. Find x and mLJM. L (4x + 10)o K (6x – 4)o J M mLJM = _____

  49. RS is an angle bisector of PRT. mPRT = 11x – 12, mSRT = 4x + 3. Find x and mPRS. P S (4x + 3)o R T mPRS = ___

  50. 1-5Angle Pairs

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