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LINES, ANGLES, AND
   PLANE SHAPES
      Geometry
Line Segments
        Line

         Line segment
Line Segments
                                  Line

                                   Line segment

When two lines are separated from each other with the same
distance in between... They are called...
Line Segments
                                  Line

                                   Line segment

When two lines are separated from each other with the same
distance in between... They are called...
Line Segments
                                  Line

                                   Line segment

When two lines are separated from each other with the same
distance in between... They are called...
Line Segments
                                  Line

                                   Line segment

When two lines are separated from each other with the same
distance in between... They are called...
Line Segments
                                  Line

                                   Line segment

When two lines are separated from each other with the same
distance in between... They are called...
Line Segments
                                      Line

                                       Line segment

When two lines are separated from each other with the same
distance in between... They are called...



                     Parallel Lines
Angles
Two line segments jointed together will form an ANGLE
       There are three different kinds of angles
Angles
Two line segments jointed together will form an ANGLE
       There are three different kinds of angles
Angles
Two line segments jointed together will form an ANGLE
       There are three different kinds of angles
Angles
Two line segments jointed together will form an ANGLE
       There are three different kinds of angles
Angles
Two line segments jointed together will form an ANGLE
         There are three different kinds of angles




 This angle has a square
         corner
Angles
Two line segments jointed together will form an ANGLE
         There are three different kinds of angles




 This angle has a square
         corner

  Right Angle
Angles
Two line segments jointed together will form an ANGLE
         There are three different kinds of angles




 This angle has a square
         corner

  Right Angle
Angles
Two line segments jointed together will form an ANGLE
         There are three different kinds of angles




 This angle has a square
         corner

  Right Angle
Angles
Two line segments jointed together will form an ANGLE
         There are three different kinds of angles




 This angle has a square   This angle is smaller
         corner            than a square corner

  Right Angle
Angles
Two line segments jointed together will form an ANGLE
         There are three different kinds of angles




 This angle has a square   This angle is smaller
         corner            than a square corner

  Right Angle          Less than Right Angle
Angles
Two line segments jointed together will form an ANGLE
         There are three different kinds of angles




 This angle has a square   This angle is smaller
         corner            than a square corner

  Right Angle          Less than Right Angle
                            Acute Angle
Angles
Two line segments jointed together will form an ANGLE
         There are three different kinds of angles




 This angle has a square   This angle is smaller
         corner            than a square corner

  Right Angle          Less than Right Angle
                            Acute Angle
Angles
Two line segments jointed together will form an ANGLE
         There are three different kinds of angles




 This angle has a square   This angle is smaller
         corner            than a square corner

  Right Angle          Less than Right Angle
                            Acute Angle
Angles
Two line segments jointed together will form an ANGLE
         There are three different kinds of angles




 This angle has a square   This angle is smaller   This angle is larger than
         corner            than a square corner        a square corner

  Right Angle          Less than Right Angle
                            Acute Angle
Angles
Two line segments jointed together will form an ANGLE
         There are three different kinds of angles




 This angle has a square   This angle is smaller     This angle is larger than
         corner            than a square corner          a square corner

  Right Angle          Less than Right Angle       Greater than Right Angle
                            Acute Angle
Angles
Two line segments jointed together will form an ANGLE
         There are three different kinds of angles




 This angle has a square   This angle is smaller     This angle is larger than
         corner            than a square corner          a square corner

  Right Angle          Less than Right Angle       Greater than Right Angle
                            Acute Angle                  Obtuse Angle
Polygons
Polygons are plane figures that are med up of line segments
and angles

Plane figures are flat figures that can be closed or not closed.
Polygons
Polygons are plane figures that are med up of line segments
and angles

Plane figures are flat figures that can be closed or not closed.




         Closed
Polygons
Polygons are plane figures that are med up of line segments
and angles

Plane figures are flat figures that can be closed or not closed.




         Closed                 Not Closed
Polygons
Polygons are closed plane figures that have 3 or more sides.

Name of a polygon tells the number of sides.
Polygons
Polygons are closed plane figures that have 3 or more sides.

Name of a polygon tells the number of sides.



    3 sides
   Triangle
Polygons
Polygons are closed plane figures that have 3 or more sides.

Name of a polygon tells the number of sides.



    3 sides               4 sides
   Triangle             Quadrilateral
Polygons
Polygons are closed plane figures that have 3 or more sides.

Name of a polygon tells the number of sides.



    3 sides               4 sides                   5 sides
   Triangle             Quadrilateral              Pentagon
Polygons
Polygons are closed plane figures that have 3 or more sides.

Name of a polygon tells the number of sides.



    3 sides               4 sides                   5 sides
   Triangle             Quadrilateral              Pentagon




        6 sides
       Hexagon
Polygons
Polygons are closed plane figures that have 3 or more sides.

Name of a polygon tells the number of sides.



    3 sides               4 sides                    5 sides
   Triangle             Quadrilateral               Pentagon




        6 sides                                 8 sides
       Hexagon                                 Octagon
Name the Polygon
Name the Polygon


Pentagon
Name the Polygon


Pentagon   Octagon
Name the Polygon


Pentagon   Octagon   Quadrilateral
Name the Polygon


Pentagon              Octagon   Quadrilateral




           Triangle
Triangles
Triangles have three sides and three angles.
There are four different types of triangles
Triangles
         Triangles have three sides and three angles.
          There are four different types of triangles




All sides have
equal length
Triangles
         Triangles have three sides and three angles.
          There are four different types of triangles




Equilateral
 Triangle


All sides have
equal length
Triangles
         Triangles have three sides and three angles.
          There are four different types of triangles




Equilateral
 Triangle


All sides have    Triangle with
equal length     one right angle
Triangles
         Triangles have three sides and three angles.
          There are four different types of triangles




Equilateral         Right
 Triangle          Triangle

All sides have    Triangle with
equal length     one right angle
Triangles
         Triangles have three sides and three angles.
          There are four different types of triangles




Equilateral         Right
 Triangle          Triangle

All sides have                      Only 2 sides
                  Triangle with
equal length                       have the same
                 one right angle
                                      length
Triangles
         Triangles have three sides and three angles.
          There are four different types of triangles
                            I stand like
                           SUPERMAN!




Equilateral         Right
 Triangle          Triangle

All sides have                              Only 2 sides
                  Triangle with
equal length                               have the same
                 one right angle
                                              length
Triangles
         Triangles have three sides and three angles.
          There are four different types of triangles
                            I stand like
                           SUPERMAN!




Equilateral         Right                   Isosceles
 Triangle          Triangle                 Triangle

All sides have                              Only 2 sides
                  Triangle with
equal length                               have the same
                 one right angle
                                              length
Triangles
         Triangles have three sides and three angles.
          There are four different types of triangles
                            I stand like
                           SUPERMAN!




Equilateral         Right                   Isosceles
 Triangle          Triangle                 Triangle

All sides have                              Only 2 sides
                  Triangle with                             All sides have
equal length                               have the same
                 one right angle                           different length
                                              length
Triangles
         Triangles have three sides and three angles.
          There are four different types of triangles
                                                                I’m Different!
                            I stand like
                           SUPERMAN!




Equilateral         Right                   Isosceles
 Triangle          Triangle                 Triangle

All sides have                              Only 2 sides
                  Triangle with                             All sides have
equal length                               have the same
                 one right angle                           different length
                                              length
Triangles
         Triangles have three sides and three angles.
          There are four different types of triangles
                                                                I’m Different!
                            I stand like
                           SUPERMAN!




Equilateral         Right                   Isosceles        Scalene
 Triangle          Triangle                 Triangle         Triangle

All sides have                              Only 2 sides
                  Triangle with                             All sides have
equal length                               have the same
                 one right angle                           different length
                                              length
Quadrilaterals
 Quadrilaterals have four sides and four angles.
There are several different types of quadrilaterals
Quadrilaterals
     Quadrilaterals have four sides and four angles.
   There are several different types of quadrilaterals




4 sides
4 right angles
Opposite sides are parallel
One pair of lines are longer
Quadrilaterals
     Quadrilaterals have four sides and four angles.
   There are several different types of quadrilaterals




  Rectangle
4 sides
4 right angles
Opposite sides are parallel
One pair of lines are longer
Quadrilaterals
     Quadrilaterals have four sides and four angles.
   There are several different types of quadrilaterals




  Rectangle
4 sides                         4 equal sides
4 right angles                  4 right angles
Opposite sides are parallel     Opposite sides are parallel
One pair of lines are longer
Quadrilaterals
     Quadrilaterals have four sides and four angles.
   There are several different types of quadrilaterals




  Rectangle                         Square
4 sides                         4 equal sides
4 right angles                  4 right angles
Opposite sides are parallel     Opposite sides are parallel
One pair of lines are longer
Quadrilaterals
There are other types of quadrilaterals
Quadrilaterals
         There are other types of quadrilaterals




4 sides
4 angles
Opposite sides are parallel
Quadrilaterals
         There are other types of quadrilaterals




Parallelogram
4 sides
4 angles
Opposite sides are parallel
Quadrilaterals
         There are other types of quadrilaterals




Parallelogram
4 sides                         4 sides
4 angles                        4 angles - 2 acute, 2 obtuse
Opposite sides are parallel     One pair of sides are parallel
Quadrilaterals
         There are other types of quadrilaterals




Parallelogram                     Trapezoid
4 sides                         4 sides
4 angles                        4 angles - 2 acute, 2 obtuse
Opposite sides are parallel     One pair of sides are parallel
Problem Solving
Draw pictures to help you solve a problem




         What would you do?
Problem Solving Continue
1. Draw a picture of an isosceles triangle
2. Label the sides
3. Look at the pictures and see what MATH you need to do
Problem Solving Continue
1. Draw a picture of an isosceles triangle
2. Label the sides
3. Look at the pictures and see what MATH you need to do
Problem Solving Continue
1. Draw a picture of an isosceles triangle
2. Label the sides
3. Look at the pictures and see what MATH you need to do




               What MATH would you do?
Problem Solving Continues
   Since you want to find out how many feet she walked
AROUND the garden, you can ADD all three sides together to
                     find the answer.




               Did you get the same answer?
Problem Solving Continues
   Since you want to find out how many feet she walked
AROUND the garden, you can ADD all three sides together to
                     find the answer.




               Did you get the same answer?
Try these...
1. Draw a square that is 1 inch on each side. Then draw a
rectangle with a width of 1 inch and a length 3 times as long.
Ho many squares will fit inside the rectangle?
Try these...
1. Draw a square that is 1 inch on each side. Then draw a
rectangle with a width of 1 inch and a length 3 times as long.
Ho many squares will fit inside the rectangle?

                           3 Squares!
Try these...
1. Draw a square that is 1 inch on each side. Then draw a
rectangle with a width of 1 inch and a length 3 times as long.
Ho many squares will fit inside the rectangle?

                           3 Squares!

2. Erin is using a piece of ribbon to make bows. Each bow uses
6 inches of ribbon. After making 5 bows, Erin has 5 inches of
ribbon left. How long was the piece of ribbon Erin started
with?
Try these...
1. Draw a square that is 1 inch on each side. Then draw a
rectangle with a width of 1 inch and a length 3 times as long.
Ho many squares will fit inside the rectangle?

                           3 Squares!

2. Erin is using a piece of ribbon to make bows. Each bow uses
6 inches of ribbon. After making 5 bows, Erin has 5 inches of
ribbon left. How long was the piece of ribbon Erin started
with?
                           35 inches!

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Chapter 9 kn - Lines, angles, and polygons

  • 1. LINES, ANGLES, AND PLANE SHAPES Geometry
  • 2. Line Segments Line Line segment
  • 3. Line Segments Line Line segment When two lines are separated from each other with the same distance in between... They are called...
  • 4. Line Segments Line Line segment When two lines are separated from each other with the same distance in between... They are called...
  • 5. Line Segments Line Line segment When two lines are separated from each other with the same distance in between... They are called...
  • 6. Line Segments Line Line segment When two lines are separated from each other with the same distance in between... They are called...
  • 7. Line Segments Line Line segment When two lines are separated from each other with the same distance in between... They are called...
  • 8. Line Segments Line Line segment When two lines are separated from each other with the same distance in between... They are called... Parallel Lines
  • 9. Angles Two line segments jointed together will form an ANGLE There are three different kinds of angles
  • 10. Angles Two line segments jointed together will form an ANGLE There are three different kinds of angles
  • 11. Angles Two line segments jointed together will form an ANGLE There are three different kinds of angles
  • 12. Angles Two line segments jointed together will form an ANGLE There are three different kinds of angles
  • 13. Angles Two line segments jointed together will form an ANGLE There are three different kinds of angles This angle has a square corner
  • 14. Angles Two line segments jointed together will form an ANGLE There are three different kinds of angles This angle has a square corner Right Angle
  • 15. Angles Two line segments jointed together will form an ANGLE There are three different kinds of angles This angle has a square corner Right Angle
  • 16. Angles Two line segments jointed together will form an ANGLE There are three different kinds of angles This angle has a square corner Right Angle
  • 17. Angles Two line segments jointed together will form an ANGLE There are three different kinds of angles This angle has a square This angle is smaller corner than a square corner Right Angle
  • 18. Angles Two line segments jointed together will form an ANGLE There are three different kinds of angles This angle has a square This angle is smaller corner than a square corner Right Angle Less than Right Angle
  • 19. Angles Two line segments jointed together will form an ANGLE There are three different kinds of angles This angle has a square This angle is smaller corner than a square corner Right Angle Less than Right Angle Acute Angle
  • 20. Angles Two line segments jointed together will form an ANGLE There are three different kinds of angles This angle has a square This angle is smaller corner than a square corner Right Angle Less than Right Angle Acute Angle
  • 21. Angles Two line segments jointed together will form an ANGLE There are three different kinds of angles This angle has a square This angle is smaller corner than a square corner Right Angle Less than Right Angle Acute Angle
  • 22. Angles Two line segments jointed together will form an ANGLE There are three different kinds of angles This angle has a square This angle is smaller This angle is larger than corner than a square corner a square corner Right Angle Less than Right Angle Acute Angle
  • 23. Angles Two line segments jointed together will form an ANGLE There are three different kinds of angles This angle has a square This angle is smaller This angle is larger than corner than a square corner a square corner Right Angle Less than Right Angle Greater than Right Angle Acute Angle
  • 24. Angles Two line segments jointed together will form an ANGLE There are three different kinds of angles This angle has a square This angle is smaller This angle is larger than corner than a square corner a square corner Right Angle Less than Right Angle Greater than Right Angle Acute Angle Obtuse Angle
  • 25. Polygons Polygons are plane figures that are med up of line segments and angles Plane figures are flat figures that can be closed or not closed.
  • 26. Polygons Polygons are plane figures that are med up of line segments and angles Plane figures are flat figures that can be closed or not closed. Closed
  • 27. Polygons Polygons are plane figures that are med up of line segments and angles Plane figures are flat figures that can be closed or not closed. Closed Not Closed
  • 28. Polygons Polygons are closed plane figures that have 3 or more sides. Name of a polygon tells the number of sides.
  • 29. Polygons Polygons are closed plane figures that have 3 or more sides. Name of a polygon tells the number of sides. 3 sides Triangle
  • 30. Polygons Polygons are closed plane figures that have 3 or more sides. Name of a polygon tells the number of sides. 3 sides 4 sides Triangle Quadrilateral
  • 31. Polygons Polygons are closed plane figures that have 3 or more sides. Name of a polygon tells the number of sides. 3 sides 4 sides 5 sides Triangle Quadrilateral Pentagon
  • 32. Polygons Polygons are closed plane figures that have 3 or more sides. Name of a polygon tells the number of sides. 3 sides 4 sides 5 sides Triangle Quadrilateral Pentagon 6 sides Hexagon
  • 33. Polygons Polygons are closed plane figures that have 3 or more sides. Name of a polygon tells the number of sides. 3 sides 4 sides 5 sides Triangle Quadrilateral Pentagon 6 sides 8 sides Hexagon Octagon
  • 37. Name the Polygon Pentagon Octagon Quadrilateral
  • 38. Name the Polygon Pentagon Octagon Quadrilateral Triangle
  • 39. Triangles Triangles have three sides and three angles. There are four different types of triangles
  • 40. Triangles Triangles have three sides and three angles. There are four different types of triangles All sides have equal length
  • 41. Triangles Triangles have three sides and three angles. There are four different types of triangles Equilateral Triangle All sides have equal length
  • 42. Triangles Triangles have three sides and three angles. There are four different types of triangles Equilateral Triangle All sides have Triangle with equal length one right angle
  • 43. Triangles Triangles have three sides and three angles. There are four different types of triangles Equilateral Right Triangle Triangle All sides have Triangle with equal length one right angle
  • 44. Triangles Triangles have three sides and three angles. There are four different types of triangles Equilateral Right Triangle Triangle All sides have Only 2 sides Triangle with equal length have the same one right angle length
  • 45. Triangles Triangles have three sides and three angles. There are four different types of triangles I stand like SUPERMAN! Equilateral Right Triangle Triangle All sides have Only 2 sides Triangle with equal length have the same one right angle length
  • 46. Triangles Triangles have three sides and three angles. There are four different types of triangles I stand like SUPERMAN! Equilateral Right Isosceles Triangle Triangle Triangle All sides have Only 2 sides Triangle with equal length have the same one right angle length
  • 47. Triangles Triangles have three sides and three angles. There are four different types of triangles I stand like SUPERMAN! Equilateral Right Isosceles Triangle Triangle Triangle All sides have Only 2 sides Triangle with All sides have equal length have the same one right angle different length length
  • 48. Triangles Triangles have three sides and three angles. There are four different types of triangles I’m Different! I stand like SUPERMAN! Equilateral Right Isosceles Triangle Triangle Triangle All sides have Only 2 sides Triangle with All sides have equal length have the same one right angle different length length
  • 49. Triangles Triangles have three sides and three angles. There are four different types of triangles I’m Different! I stand like SUPERMAN! Equilateral Right Isosceles Scalene Triangle Triangle Triangle Triangle All sides have Only 2 sides Triangle with All sides have equal length have the same one right angle different length length
  • 50. Quadrilaterals Quadrilaterals have four sides and four angles. There are several different types of quadrilaterals
  • 51. Quadrilaterals Quadrilaterals have four sides and four angles. There are several different types of quadrilaterals 4 sides 4 right angles Opposite sides are parallel One pair of lines are longer
  • 52. Quadrilaterals Quadrilaterals have four sides and four angles. There are several different types of quadrilaterals Rectangle 4 sides 4 right angles Opposite sides are parallel One pair of lines are longer
  • 53. Quadrilaterals Quadrilaterals have four sides and four angles. There are several different types of quadrilaterals Rectangle 4 sides 4 equal sides 4 right angles 4 right angles Opposite sides are parallel Opposite sides are parallel One pair of lines are longer
  • 54. Quadrilaterals Quadrilaterals have four sides and four angles. There are several different types of quadrilaterals Rectangle Square 4 sides 4 equal sides 4 right angles 4 right angles Opposite sides are parallel Opposite sides are parallel One pair of lines are longer
  • 55. Quadrilaterals There are other types of quadrilaterals
  • 56. Quadrilaterals There are other types of quadrilaterals 4 sides 4 angles Opposite sides are parallel
  • 57. Quadrilaterals There are other types of quadrilaterals Parallelogram 4 sides 4 angles Opposite sides are parallel
  • 58. Quadrilaterals There are other types of quadrilaterals Parallelogram 4 sides 4 sides 4 angles 4 angles - 2 acute, 2 obtuse Opposite sides are parallel One pair of sides are parallel
  • 59. Quadrilaterals There are other types of quadrilaterals Parallelogram Trapezoid 4 sides 4 sides 4 angles 4 angles - 2 acute, 2 obtuse Opposite sides are parallel One pair of sides are parallel
  • 60. Problem Solving Draw pictures to help you solve a problem What would you do?
  • 61. Problem Solving Continue 1. Draw a picture of an isosceles triangle 2. Label the sides 3. Look at the pictures and see what MATH you need to do
  • 62. Problem Solving Continue 1. Draw a picture of an isosceles triangle 2. Label the sides 3. Look at the pictures and see what MATH you need to do
  • 63. Problem Solving Continue 1. Draw a picture of an isosceles triangle 2. Label the sides 3. Look at the pictures and see what MATH you need to do What MATH would you do?
  • 64. Problem Solving Continues Since you want to find out how many feet she walked AROUND the garden, you can ADD all three sides together to find the answer. Did you get the same answer?
  • 65. Problem Solving Continues Since you want to find out how many feet she walked AROUND the garden, you can ADD all three sides together to find the answer. Did you get the same answer?
  • 66. Try these... 1. Draw a square that is 1 inch on each side. Then draw a rectangle with a width of 1 inch and a length 3 times as long. Ho many squares will fit inside the rectangle?
  • 67. Try these... 1. Draw a square that is 1 inch on each side. Then draw a rectangle with a width of 1 inch and a length 3 times as long. Ho many squares will fit inside the rectangle? 3 Squares!
  • 68. Try these... 1. Draw a square that is 1 inch on each side. Then draw a rectangle with a width of 1 inch and a length 3 times as long. Ho many squares will fit inside the rectangle? 3 Squares! 2. Erin is using a piece of ribbon to make bows. Each bow uses 6 inches of ribbon. After making 5 bows, Erin has 5 inches of ribbon left. How long was the piece of ribbon Erin started with?
  • 69. Try these... 1. Draw a square that is 1 inch on each side. Then draw a rectangle with a width of 1 inch and a length 3 times as long. Ho many squares will fit inside the rectangle? 3 Squares! 2. Erin is using a piece of ribbon to make bows. Each bow uses 6 inches of ribbon. After making 5 bows, Erin has 5 inches of ribbon left. How long was the piece of ribbon Erin started with? 35 inches!

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