1. GEOMETRY!!!

2. Points  A point is an end of a line segment.  It is an exact location in space.   It is represented by a small dot. Point A A

3. Lines  A line is a collection of points in a straight path that extends in two directions without end.  It is represented by a straight line with two arrowheads to indicate that the line extends without end in two directions. A Line l or AB B..

4. Line Segments  The line segment or segment AB consists of the endpoints A and B, and all points that are between A and B.  A line segment is a part of a line with two endpoints. AB Segment AB

5. Ray  A ray is part of a line having only one endpoint. AB Ray AB

6. Planes A plane extends in two dimensions.  A plane is an endless flat surface. It is usually represented by a shape that looks like a tabletop or wall. You must imagine that the plane extends without end even though the drawing of a plane appears to have edges. A B C M Plane M or plane ABC

7. Angles  An angle is two rays having a common endpoint.... X W Y

8. Classifications of Angles  Angles are measured in degrees.  A degree is 1/360 of a complete rotation.  To measure the number of degrees in an angle, a protractor or an angle ruler is used.

9. Classifications of Angles  Angles are classified according to their measures as  acute  right  obtuse  straight angles

10. Acute Angle  An acute angle forms an angle less than a right angle.  An acute angle measures greater than 0° and less than 90°.

11. Right Angle  A right angle is an angle of 90 degrees. degrees  Lines that are at a right angle to each other are perpendicular. perpendicular  A right angle is an angle that forms a square corner.

12. Obtuse Angle  An obtuse angle forms an angle greater than a right angle.  An obtuse angle measures greater than 90° and less than 180°.

13. Reflex Angle  A reflex angle forms an angle greater than a straight angle.  An reflex angle measures greater than 180° and less than 360°.

14. Straight Angle  Angles equal to two right angles (180°) are called straight angles.

15. Measuring, calculating and drawing angles...

16. What do we use to help us? A protractor Here is a standard protractor like you use in the classroom.

17. When we use a protractor, we need to line it up correctly. YYYYou need to make sure the protractor is lined up correctly. IIIIs this ready to measure the angle?

18. Were you right......................it wasn’t LLLLook for the upside down ‘T’ in the middle of the straight line on your protractor. TTTThis needs to be exactly on the vertex of your angle.

19. We need to remember..... It doesn’t matter which way round the angle is, you ALWAYS need to line the upside down ‘T’ to the vertex of the angle.

20. Now you are ready. Read from the 0°, and follow the inner set of numbers.

21. Once you reach 30° you need to be careful!!! You then need to look at the 1° markings on the outer set of numbers.

22. What does it measure? This angle measures 35°.

23. Measuring with Angle Rulers

24. Triangles  A triangle is a polygon with three sides.  Triangles may be classified according to the measure of the angles.  Triangles may also be classified according to the measure of the sides.

25. Acute Triangles  An acute triangle has three acute angles.  Equilateral triangles are acute triangles.

26. Right Triangles  A right triangle has one right angle and two acute angles.

27. Obtuse Triangles  An obtuse triangle has one obtuse angle and two acute angles.

28. Equilateral Triangle  An equilateral triangle has all sides the same length.

29. Isosceles Triangle  An isosceles triangle has two sides that are the same length and two interior angles that are the same.

30. Scalene Triangle  The sides of a scalene triangle are all different lengths. triangle  A right triangle can be a scalene triangle (but not all right triangles are scalene triangles).

31. Polygons  A polygon is a plane closed figure with segments as sides.  A polygon is a many-sided figure with straight edges.

32. Examples of Polygons

33. The Figure Below is not a Polygon …  The figure below is not a polygon, since it is not a closed figure.

34. The Figure Below is not a Polygon …  The figure below is not a polygon, since it is not made of line segments.

35. The Figure Below is not a Polygon …  The figure below is not a polygon, since its sides do not intersect in exactly two places each.

36. Quadrilaterals  A quadrilateral is a polygon with four sides.  Properties of a parallelogram include: 1. A diagonal divides the parallelogram into two congruent triangles. 2. The opposite sides of a parallelogram are congruent. 3. The opposite angles of a parallelogram are congruent.

37. Examples of Quadrilaterals Rectangles Squares ParallelogramsRhombus Trapezoid

38. Parallelograms  A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel.  The opposite sides are parallel to each other and the have the same length.  The sum of the angles of a parallelogram is 360 degrees.

39. Rectangles  A rectangle is a parallelogram with four right angles.  The opposite sides have the same length.  The sum of the angles of a rectangle is 360 degrees.

40. Squares  A square is a rectangle in which each side is the same length.  Since a square is a rectangle, the square has all the properties of the rectangle and the parallelogram.  The sum of the angles of a square is 360 degrees.

41. Rhombus  A rhombus is a type of parallelogram in which each side is the same length.  Opposite angles of a rhombus are congruent.  The sum of the angles of a rhombus is 360 degrees.  Since a rhombus is a parallelogram, the rhombus has all the properties of a parallelogram.

42. Trapezoids  A trapezoid is a quadrilateral with exactly one pair of parallel sides.  The parallel sides are called bases  and the non-parallel sides are called legs.  The sum of the angles of a trapezoid is 360 degrees.

43. Kites  A kite is a quadrilateral shaped like a diamond in which the two pairs of adjacent sides have the same length.

44. Symmetry  A figure exhibits symmetry when part of the figure is the mirror image of another part of the figure.

45. Reflection  An object has reflection (or line symmetry) when one side of the figure is a mirror image of the other across the line of symmetry.  For example: a heart

46. Lines of Symmetry

47. 1. Where is the line of symmetry?

48. 2. Where is the line of symmetry?

49. 3. Where are the lines of symmetry?

50. Reflection, Rotation, or Translation 1.

51. Reflection, Rotation, or Translation 2.

52. Reflection, Rotation, or Translation 3.

53. Reflection, Rotation, or Translation 4.

54. Reflection, Rotation, or Translation 5.

55. Reflection, Rotation, or Translation 6.

56. Congruent Figures . Two polygons are congruent if the measures of corresponding angles are the same and if the lengths of corresponding sides are the same.

58. Scalene Triangle  scalene (no sides congruent),

59. Drawing Triangles

60. Measuring Triangles

61. Some Questions …  Can a right triangle can have an obtuse angle? Why or why not?  Can an obtuse triangle have more than one obtuse angle? Why or why not?  What type of angles are the two angles other than the right angle in a right triangle?  What type of angles are the two angles other than the obtuse angle in an obtuse triangle?

63. Using Regular Polygons in Our World

65. Lines of Symmetry  A line of symmetry is a line that divides a figure into congruent halves, each of which is the reflection image of the other.

66. Translations = Slides  A translation (slide) is a transformation in which an image is formed by moving every point on a figure the same distance in the same direction.

67. Reflections = Flips  A reflection (flip) is a transformation in which a figure is flipped over a line called the line of reflection. All corresponding points in the image and pre-image are equidistant from the line of reflection.

68. Rotations = Turns  A rotation (turn) is a transformation in which the image is formed by turning its pre-image about a point.

69. Congruency  Two figures are said to be congruent if they have exactly the same size and shape.  A kite is a quadrilateral with two distinct pairs of adjacent congruent sides.

70. Similar Figures  Two figures are said to be similar if they have exactly the same shape, but not necessarily the same size.

71. Let’s Try This!  Two figures can be combined to form a new shape.  A polygon may be subdivided into two or more figures.  Let’s divide a polygon into familiar figures.

72. Regular Polygons & Symmetry

74. Three-Dimensional Figures  Three-dimensional figures are solid figures, or simply solids.  Solids enclose a region of space.  Solids are classified by the types of surfaces they have.  These surfaces may be flat, curved, or both.

75. Cylinders  A cylinder is a solid bounded by two congruent and parallel circular regions joined by a curved surface whose cross- section perpendicular to the axis is always a circle congruent to the bases.

76. Cones  A cone is a solid bounded by a circular base and a curved surface with one vertex.  Rectangular solids are called rectangular prisms. Rectangular prisms have bases that are rectangles. A rectangular prism in which all the faces are congruent squares is a cube.  A cube is a solid with six congruent square faces where every face is a square and every edge is the same length. A cube has 6 faces and 12 edges. A square pyramid is a polyhedron whose base is a square and whose other faces are triangles that share a common vertex. A rectangular prism is a solid in which all six faces are rectangles with three pair of parallel congruent opposite faces.

77. Cubes  A cube is a solid with six congruent square faces where every face is a square and every edge is the same length.  A cube has 6 faces and 12 edges.

78. Square Pyramid  A square pyramid is a polyhedron whose base is a square and whose other faces are triangles that share a common vertex.

79. Faces

80. Edges

81. Vertex

82. Rectangular Prisms  Rectangular solids are called rectangular prisms. Rectangular prisms have bases that are rectangles.  A rectangular prism in which all the faces are congruent squares is a cube.  A rectangular prism is a solid in which all six faces are rectangles with three pair of parallel congruent opposite faces.

84. Circles  A circle is a set of points on a flat surface (plane) that are the same distance from a given point called the center.  The center is not a part of the circle itself.

85. Diameter  A diameter is a chord that goes through the center of the circle.  Circumference is the distance around or perimeter of a circle. The circumference of a circle is slightly longer than three times its diameter.  

86. Radius  A radius is a line segment from the center of a circle to any point on the circle.  The diameter is twice the size of the radius and the radius is half of a diameter.

87. Chords  A chord is a line segment connecting any two points on the circle.

88. Circumference  Circumference is the distance around or perimeter of a circle.  The circumference of a circle is slightly longer than three times its diameter.

89. Let’s Think …  What size relationship exists between a diameter and a radius?

90. Let’s Think …  How is the circumference of a circle estimated?

92. A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same.  The following are examples of regular polygons:  The following are not examples of regular polygons: 