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Geometry

earth. to measure. Geometry. Geo + metry. Three basic terms:. point. line. plane. A. Figure. point A. Name. Symbol. A. A point shows an exact location in space and is represented by a dot. Description. B. C. BC. Figure. line BC. Name. Symbol.

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Geometry

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  1. earth to measure Geometry Geo + metry

  2. Three basic terms: point line plane

  3. A Figure point A Name Symbol A A point shows an exact location in space and is represented by a dot. Description

  4. B C BC Figure line BC Name Symbol A line is a set of points that extends infinitely in both directions. Description

  5. A C B Figure plane ABC Name Symbol plane ABC

  6. A C B Figure A plane is a flat surface that extends infinitely in all directions. Description

  7. G H GH Figure segment GH Name Symbol A segment is part of a line consisting of two endpoints and all the points between them. Description

  8. J K JK Figure ray JK Name Symbol A ray is part of a line consisting of one endpoint and extending infinitely through a second named point. Description

  9. Example 1 Name all of the possible points, lines, planes, segments, and rays in the figure using the letters X, Y, and Z. X Z Y

  10. Lines: XY, YZ, XZ Segments: XY, YZ, XZ Rays: XY, YX, YZ, ZY, XZ, ZX X Z Y Points: X, Y, Z Planes: plane XYZ

  11. AB, BC, or AC Example Name a line. E D A B C

  12. BA, BD, BE, and BC Example Name four rays with endpoint B. E D A B C

  13. No, the endpoint is listed first. EB is not shown in the figure. Example Are rays BE and EB the same ray? E D A B C

  14. Angle • An angle is a geometric figure made up of two rays that have a common endpoint. The common endpoint is the vertex. Each of the rays is a side of the angle.

  15. A B C

  16. Measuring an Angle • Position the center point of the protractor on the vertex of the angle to be measured. • Align the zero degree mark on the protractor with one side of the angle.

  17. Measuring an Angle 3. Read the number of degrees to the other side of the angle on the protractor.

  18. mX < 90° X acute angle

  19. mY = 90° Y right angle

  20. 90° < mZ< 180° Z obtuse angle

  21. mW = 180° W straight angle

  22. 6; ABD, DBE, EBC, ABE, DBC, and ABC Example How many angles are there in the figure? List them. E D A B C

  23. Example Classify ABE as acute, obtuse, right, or straight. E D A B C right

  24. Example Classify DBE as acute, obtuse, right, or straight. E D A B C acute

  25. Example Classify ABC as acute, obtuse, right, or straight. E D A B C straight

  26. Example Classify DBC as acute, obtuse, right, or straight. E D A B C obtuse

  27. m DAE = 50° Example 2 Find the measure of DAE. C D B E A

  28. m CAE = 125° Example 2 Find the measure of CAE. C D B E A

  29. m BAC = 55° Example 2 Find the measure of BAC. C D B E A

  30. m BAE = 180° Example 2 Find the measure of BAE. C D B E A

  31. GEH, GEF, FEH, H, FGE Example 3 Name all acute angles. E 35° 120° 25° F H G

  32. F Example 3 Name a right angle. E 35° 120° 25° F H G

  33. EGH Example 3 Name an obtuse angle. E 35° 120° 25° F H G

  34. FGH Example 3 Name a straight angle. E 35° 120° 25° F H G

  35. m XYZ + 23 = 57 – 23 – 23 m XYZ = 34° Example 4 If m WYZ = 23°, write and solve an equation to find mXYW. X 57° W 23° Y Z

  36. Example If DBC is 138°, what is the measure of ABD? E D A B C 42°

  37. Example If DBC is 138°, what is the measure of DBE? E D A B C 48°

  38. Exercise How many lines can be drawn to connect two different points? 1

  39. Exercise How many lines can be drawn to connect any two of three points that are not on the same line? 3

  40. Exercise How many lines can be drawn to connect any two of four points, no three of which are on the same line? 6

  41. Exercise How many lines can be drawn to connect any two of five points, no three of which are on the same line? 10

  42. Exercise How many lines can be drawn to connect any two of six points, no three of which are on the same line? 15

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