1 / 72

Understanding Points, Lines, and Angles in Geometry: Key Concepts and Practice

This study guide covers the fundamental concepts of geometry, including points, lines, planes, segments, and angles. Students will learn about collinearity, coplanarity, and how to measure segments and angles. The guide includes multiple practice questions on identifying collinear points, marking congruent segments, and calculating distances and midpoints both on a number line and coordinate plane. Additionally, it covers naming angles and the angle addition postulate to develop a deep understanding of geometric relationships.

crescent
Télécharger la présentation

Understanding Points, Lines, and Angles in Geometry: Key Concepts and Practice

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related