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Chapter 1 Slides

Chapter 1 Slides. 1.2 – Points, Lines, and Planes (2 days). A definition uses known words to describe a new word. In geometry, points, lines, and planes are undefined terms.

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Chapter 1 Slides

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  1. Chapter 1 Slides

  2. 1.2 – Points, Lines, and Planes (2 days)

  3. A definition uses known words to describe a new word. In geometry, points, lines, and planes are undefined terms. Point. Technically, it has no size, but we use a dot that has size to represent it. You use a capital letter to label it. Such as Point A All figures are made of points. This is a LINE. It goes both ways, forever without ending. Once again, it has no thickness, but we use a picture with thickness to describe it. Arrows on both ends say it goes on forever.

  4. PLANE, goes on forever, once again has no thickness. Even though it goes on forever, we usually use a parallelogram shape to draw it. A K I M To label it, a capital cursive letter can be used, or you can use three points that don’t line up (also known as non-collinear points)

  5. D U C K S Collinear points, points all in one line. Noncollinear points, points NOT all in one line. Coplanar points, points all in one plane. Noncoplanar points, points NOT all in one plane.

  6. Name all the coplanar points. B A C D E F H G

  7. R I T B F This is a ray This is a line segment, it is a segment, or part of a line T, R are ENDPOINTS ORDER MATTERS

  8. l M N O OPPOSITE RAYS – are called opposite rays cuz N is between M and O.

  9. Name four coplanar points ABCD or FGHI or some other combination that works l P B Name three collinear points A DAB or AEF or GFJ D C What is the intersection of line l and plane P? E Point A Q G I Which plane has points F,H,I? F J Plane Q H

  10. Two or more geometric figures intersect if they have one or more points in common. The intersection of the figures is the set of points the figures have in common. Draw three noncollinear points A, B, C on plane P. Draw line l not on plane P going through point C.

  11. Draw three planes M, N, P meeting at point P. Draw three planes M, N, P meeting on line l. In 3-D, sometimes it helps to imagine a box, or look around the room (but not during a test)

  12. 1.3 Segments and Their Measures (1 day)

  13. Postulate \ Axiom – A rule that is accepted WITHOUT PROOF. Postulate 1 – Ruler Postulate The points on a line can be matched one to one with the real numbers. The real number that corresponds to a point is the coordinate of the point. The distance between points A and B, written as AB, is the absolute value of the difference between the coordinates of A and B. AB is also called the length of AB. A B -1 0 1

  14. Find the distance between the points Order of subtraction doesn’t matter. But doing right minus left keeps things positive. Where your ruler is doesn’t matter. Two points are the same distance apart no matter how you line up the ruler.

  15. AC A B C AB BC SEGMENT ADDITION POSTULATE If B is BETWEEN A and C, then AB + BC = AC. Also If AB + BC = AC, then B is between A and C

  16. B E O A X T

  17. DS = 30 DU = 5 KS = 7 UC = .5CK D U C K S UK = UC = DC = US = boardwork

  18. (x2,y2) (3,2) (x1,y1) (-4,-2)

  19. (-5, -2) (4, 1) x1y1x2y2

  20. 5 5 H S T R Congruence is shown with marks. The marks say that they are the same size and shape Equals means they have equal length, number value. They are equivalent. Definition of congruent segments: Congruent segments have equal lengths

  21. Find the distance between Mr. Kim and each food location. (0, 12) (8, 6) (0, 0) (16, 0) (8, 0) From where Mr. Kim starts, if he goes to In-N-Out, Der Veener, and Carl’s, and back to where he started, how far does he walk? Does the “King” scare you too?

  22. 1.4 – Angles and Their Measures (2 days)

  23. L A E N 1 G S Angles are formed by two rays with the same initial point. Two rays are called the sides. The initial point is called the vertex

  24. If two angles are congruent, their measures are equal. If the measure of two angles are equal, they are congruent D R 1 2 U E C X

  25. Protractor Postulate A O B Consider a point A on one side of OB. The rays of the form OA can be matched one to one with the real numbers from 0 to 180. The measure of AOB is equal to the absolute value of the difference between the real numbers for OA and OB.

  26. Acute – Angle is between 0 and 90 degrees Right – Angle is exactly 90 degrees Obtuse – Angle is between 90 and 180 degrees 90 180 0 Straight – Angle is 180 degrees

  27. A point is in the interior of an angle if it is between points that lie on each side of the angle. A points is in the exterior of an angle if it is not on the angle or its interior D U C

  28. B U C D T R O Y Adjacent angles, share common side and vertex, but share NO interior points.

  29. C O B A

  30. Find the measure of the unknown angles, state if they are acute, right, or obtuse. 1 2 3 4 A D C B E F 1 76o

  31. Draw angle ABC that is 90o. Draw right angle DBF so that angle ABF and DBA is 45o and A is in the interior of angle DBF and F is in the interior of angle ABC.

  32. Draw a right angle KIM. Draw angle JIQ such that M is in the interior of angle JIQ and Q is in the interior of KIM and JIM is 30 degrees and MIQ is 60 degrees

  33. 1.5 – Segment and Angle Bisectors (2 days)

  34. D B A C E SEGMENT BISECTOR – A line, segment, or ray that INTERSECTS THE SEGMENT AT THE MIDPOINT! The MIDPOINT of a segment divides the segment into TWO congruent parts.

  35. What coordinate is in the MIDDLE of these two points? (-3, -2) (5, -1) x1y1x2y2

  36. Find the midpoint.

  37. Given an endpoint and the midpoint, find the other endpoint. A is an endpoint, M is a midpoint A (5, -2) M (3, 6) B (x, y) A (2, 6) M (-1, 4) B (x, y)

  38. B A T R ANGLE BISECTOR – is a ray that divides an angle into two adjacent angles that are congruent.

  39. A A D D B B C C

  40. Constructing a perpendicular bisector. 1) Point on one end, arc up and down. 2) Switch ends and do the same 3) Draw line through intersection This is DIFFERENT from book (slightly).

  41. Bisect an angle 1) Draw an arc going across both sides of the angle. 2) Put point on one intersection, pencil on other, draw an arc so that it goes past at least the middle. 3) Flip it around and to the same. 4) Line from vertex to intersection.

  42. 1.7 – Introduction to Perimeter, Circumference, and Area

  43. Square A = s2P = 4s s Rectangle A = lwP = 2l+2w l w

  44. Circumference is the distance around the circle. (Like perimeter) C = πd = 2πr LIKE THE CRUST PIZZA PART Area of a circle: A = πr2

  45. Fake sun has a radius of .5 centimeters. Find the circumference and area of fake sun.

  46. Find Perimeter\Circumference, and Area for each shape 13 cm 15 cm 5 ft Scale 12 cm 14 cm 3 ft 3 ft 3 in 6 ft

  47. Find the area and perimeter 12 cm 17 cm 8 cm 8 cm 12 cm 15 cm

  48. Find the area of the figure described Find the area of a circle with diameter 10 m Find the area of a rectangle with base 4 ft and height 2 ft Find the area of a triangle with base 2 in and height 6 in Find the area of a square with perimeter 8 miles Write on board

  49. Finding Area Area of triangle with vertices (-1,2); (4,2); and (2, -2)

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