Geometry Review
Solid Shapes <ul><li>Solid shapes have three parts:  </li></ul><ul><li>faces, edges, and vertices. Look at the shape below...
Solid Shapes A  cylinder  has 2 faces and 2 edges. edge face
Solid Shapes A  cube  has 6 faces, 12 edges and 8 vertices. face vertex edge
Solid Shapes A  cone  has 1 face, 1 vertex and 1 edge. face edge face(on bottom)
Solid Shapes A  square pyramid  has 5 faces, 8 edges, and 5 vertices. face vertex edge
Solid Shapes A sphere has no faces, edges, or vertices, but we love it anyway!
Solid Shapes A  rectangular prism  has 6 faces, 12 edges, and 8 vertices, just like a square. face edge vertex
Lines and Angles We learned about 3 kinds of lines: lines line segments rays. line segment-  has two endpoints line -  goe...
Lines and Angles An angle is two rays connected at a vertex. We learned about 3 kinds of angles: right obtuse acute obtuse...
Lines and Angles <ul><li>There are 3 ways lines can be related: parallel intersecting perpendicular </li></ul>parellel -  ...
Circles <ul><li>Circles are named by their center point. They have diameters, which are lines that cross through the cente...
Circles <ul><li>The name of this circle is  B. </li></ul>B
Circles <ul><li>This is a  radius . It is named  AB  or  BA . </li></ul>B A
Circles <ul><li>Below is the  diameter  of the circle. It is named  CD  or  DC . </li></ul>B C D
Circles <ul><li>A diameter is made up of two radii. So to find the length of the diameter, you just double the length of a...
Polygons <ul><li>A polygon is a  closed figure  with  straight sides . The are classified by the number of sides they have...
<ul><li>These are all  triangles  because they have 3 sides.  </li></ul>Polygons
<ul><li>How many triangles are in this picture ?   </li></ul>Polygons
<ul><li>These are all  quadrilaterals  because they have 4 sides .   </li></ul>Polygons
<ul><li>These are all  pentagons  because they have 5 sides. </li></ul>Polygons
<ul><li>These are all  hexagons  because they have 6 sides.  </li></ul>Polygons
<ul><li>These are all  octagons  because they have 8 sides.  </li></ul>Polygons
Triangles <ul><li>Triangles are classified in two ways: by the length of their sides, and by their angles. </li></ul><ul><...
<ul><li>These are all  right  triangles because they each have one right angle.  </li></ul>Triangles
<ul><li>These are all  acute  triangles because all of the angles are acute.  </li></ul>Triangles
<ul><li>These are all  obtuse  triangles because the have one obtuse angle.  </li></ul>Triangles
<ul><li>These are all  equilateral  triangles because all 3 sides are congruent. </li></ul>Triangles
<ul><li>These are all  isosceles  triangles because they have 2 congruent sides.  </li></ul>Triangles
<ul><li>These are all  scalene  triangles because none of the sides are congruent. </li></ul>Triangles
Quadrilaterals <ul><li>Quadrilateral are 4-sided figures. Some special quadriltaterals are: </li></ul><ul><li>Square- 4 si...
quadrilateral trapezoid parallelogram rhombus rectangle square square
Quadrilaterals Image found at:  www.cimt.plymouth.ac.uk/.../bk8i15/bk8_15i4.htm
<ul><li>These are all rhombii (the plural of rhombus) because they have: </li></ul><ul><li>2 sets of parallel sides </li><...
<ul><li>These are all squares because they have: </li></ul><ul><li>2 sets of parallel sides </li></ul><ul><li>4 congruent ...
<ul><li>These are all trapezoids because they all have: </li></ul><ul><li>1 set of parallel sides </li></ul>Quadrilaterals
<ul><li>These are all rectangles because they all have: </li></ul><ul><li>2 sets of parallel sides </li></ul><ul><li>2 set...
<ul><li>These are all parallelograms because they all have: </li></ul><ul><li>2 sets of parallel sides </li></ul><ul><li>2...
Symmetry <ul><li>This shape has symmetry. </li></ul><ul><li>This shape does not. </li></ul>A shape has symmetry if you can...
<ul><li>The shape below does not have a line of symmetry. </li></ul>Symmetry
<ul><li>The shape below has two lines of symmetry. </li></ul>Symmetry
Congruence <ul><li>Shapes are  congruent  if the are same size and shape.  </li></ul><ul><li>These two shapes are congruen...
<ul><li>The shapes below are also congruent. It’s just that they are not facing the same way. </li></ul>Congruence
<ul><li>Two shapes are  similar  if the are the same shape but not the same size. </li></ul>Similarity These two shapes ar...
<ul><li>Think about this - all circles and squares are either  congruent  or  similar. </li></ul>Similarity
Transformations <ul><li>Transformations are ways of moving shapes. The three we learned are: </li></ul><ul><li>flips </li>...
Transformations The thing to remember about tranformations is this: they don't change the size or shape of the original po...
<ul><li>A flip is like a reflection. A shape flips over itself.  </li></ul>Transformations These are both  flips .
<ul><li>A shape is turned when it rotates around a corner. </li></ul>Transformations These are all  turns .
<ul><li>Sliding  means moving in any direction without turning it or flipping it.  These are all  slides . </li></ul>Trans...
<ul><li>When shapes tessellate, they fit together perfectly to cover a page. For example, hexagons tessellate nicely . </l...
<ul><li>But lots of other shapes tessellate as well . In fact, there are artists who specialize in creating tessellations....
<ul><li>You don’t have to be an artist to make a tessellation. Just click on the picture below to find directions for maki...
<ul><li>Below are some websites where you can view some tessellations and learn more about them.  </li></ul>Tessellations ...
Some Helpful Websites http://www.mathleague.com/help/geometry/polygons.htm http://www.mathsisfun.com/geometry/index.html
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Geometry Review

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Review of all the concepts we learned in our geometry unit

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  1. 1. Geometry Review
  2. 2. Solid Shapes <ul><li>Solid shapes have three parts: </li></ul><ul><li>faces, edges, and vertices. Look at the shape below to see what each is. </li></ul>face vertex edge Note: Faces must be flat!
  3. 3. Solid Shapes A cylinder has 2 faces and 2 edges. edge face
  4. 4. Solid Shapes A cube has 6 faces, 12 edges and 8 vertices. face vertex edge
  5. 5. Solid Shapes A cone has 1 face, 1 vertex and 1 edge. face edge face(on bottom)
  6. 6. Solid Shapes A square pyramid has 5 faces, 8 edges, and 5 vertices. face vertex edge
  7. 7. Solid Shapes A sphere has no faces, edges, or vertices, but we love it anyway!
  8. 8. Solid Shapes A rectangular prism has 6 faces, 12 edges, and 8 vertices, just like a square. face edge vertex
  9. 9. Lines and Angles We learned about 3 kinds of lines: lines line segments rays. line segment- has two endpoints line - goes on in both directions forever ray - has one endpoint, goes on in one way forever
  10. 10. Lines and Angles An angle is two rays connected at a vertex. We learned about 3 kinds of angles: right obtuse acute obtuse - larger(more open) than a right angle right - makes a perfect corner(90  ) acute - smaller(more closed) than a right angle
  11. 11. Lines and Angles <ul><li>There are 3 ways lines can be related: parallel intersecting perpendicular </li></ul>parellel - never intersect intersecting - cross at a point perpendicular - intersect and form right angles
  12. 12. Circles <ul><li>Circles are named by their center point. They have diameters, which are lines that cross through the center point and go from one side of the circle to the other. They also have radii (plural of radius) which go from the center point to a point on the circle. </li></ul>
  13. 13. Circles <ul><li>The name of this circle is B. </li></ul>B
  14. 14. Circles <ul><li>This is a radius . It is named AB or BA . </li></ul>B A
  15. 15. Circles <ul><li>Below is the diameter of the circle. It is named CD or DC . </li></ul>B C D
  16. 16. Circles <ul><li>A diameter is made up of two radii. So to find the length of the diameter, you just double the length of a radius. </li></ul>B C D 2” If the length of the radius is 2 inches, the length of the diameter is 4 inches.
  17. 17. Polygons <ul><li>A polygon is a closed figure with straight sides . The are classified by the number of sides they have. </li></ul><ul><li>3 sides – triangle 4 sides – quadrilateral 5 sides – pentagon 6 sides – hexagon 8 sides - octagon </li></ul>If all of the sides are the same length, it is called a regular polygon. If they are not, it is called an irregular polygon.
  18. 18. <ul><li>These are all triangles because they have 3 sides. </li></ul>Polygons
  19. 19. <ul><li>How many triangles are in this picture ? </li></ul>Polygons
  20. 20. <ul><li>These are all quadrilaterals because they have 4 sides . </li></ul>Polygons
  21. 21. <ul><li>These are all pentagons because they have 5 sides. </li></ul>Polygons
  22. 22. <ul><li>These are all hexagons because they have 6 sides. </li></ul>Polygons
  23. 23. <ul><li>These are all octagons because they have 8 sides. </li></ul>Polygons
  24. 24. Triangles <ul><li>Triangles are classified in two ways: by the length of their sides, and by their angles. </li></ul><ul><li>Sides </li></ul><ul><li>Equilateral – all 3 sides the same </li></ul><ul><li>Isosceles – 2 sides the same </li></ul><ul><li>Scalene – no side the same </li></ul><ul><li>Angles </li></ul><ul><li>Right – one right angle </li></ul><ul><li>Obtuse – one obtuse angle </li></ul><ul><li>Acute – all three angles acute </li></ul>
  25. 25. <ul><li>These are all right triangles because they each have one right angle. </li></ul>Triangles
  26. 26. <ul><li>These are all acute triangles because all of the angles are acute. </li></ul>Triangles
  27. 27. <ul><li>These are all obtuse triangles because the have one obtuse angle. </li></ul>Triangles
  28. 28. <ul><li>These are all equilateral triangles because all 3 sides are congruent. </li></ul>Triangles
  29. 29. <ul><li>These are all isosceles triangles because they have 2 congruent sides. </li></ul>Triangles
  30. 30. <ul><li>These are all scalene triangles because none of the sides are congruent. </li></ul>Triangles
  31. 31. Quadrilaterals <ul><li>Quadrilateral are 4-sided figures. Some special quadriltaterals are: </li></ul><ul><li>Square- 4 sides the same; 4 right angles; 2 sets parallel sides </li></ul><ul><li>Rectangle – 4 right angles; 2 sets parallel sides </li></ul><ul><li>Parallelogram – 2 sets parallel sides </li></ul><ul><li>Rhombus – 2 sets parallel sides; 4 sides the same </li></ul><ul><li>Trapezoid – 1 set parallel sides </li></ul>
  32. 32. quadrilateral trapezoid parallelogram rhombus rectangle square square
  33. 33. Quadrilaterals Image found at: www.cimt.plymouth.ac.uk/.../bk8i15/bk8_15i4.htm
  34. 34. <ul><li>These are all rhombii (the plural of rhombus) because they have: </li></ul><ul><li>2 sets of parallel sides </li></ul><ul><li>4 congruent sides </li></ul>Quadrilaterals
  35. 35. <ul><li>These are all squares because they have: </li></ul><ul><li>2 sets of parallel sides </li></ul><ul><li>4 congruent sides </li></ul><ul><li>4 right angles </li></ul>Quadrilaterals
  36. 36. <ul><li>These are all trapezoids because they all have: </li></ul><ul><li>1 set of parallel sides </li></ul>Quadrilaterals
  37. 37. <ul><li>These are all rectangles because they all have: </li></ul><ul><li>2 sets of parallel sides </li></ul><ul><li>2 sets of congruent sides </li></ul><ul><li>4 right angles </li></ul>Quadrilaterals
  38. 38. <ul><li>These are all parallelograms because they all have: </li></ul><ul><li>2 sets of parallel sides </li></ul><ul><li>2 sets of congruent sides </li></ul>Quadrilaterals
  39. 39. Symmetry <ul><li>This shape has symmetry. </li></ul><ul><li>This shape does not. </li></ul>A shape has symmetry if you can draw a line so that when the shape is folded ont the line, the sides will match exactly.
  40. 40. <ul><li>The shape below does not have a line of symmetry. </li></ul>Symmetry
  41. 41. <ul><li>The shape below has two lines of symmetry. </li></ul>Symmetry
  42. 42. Congruence <ul><li>Shapes are congruent if the are same size and shape. </li></ul><ul><li>These two shapes are congruent. </li></ul><ul><li>These two shapes are not. </li></ul>
  43. 43. <ul><li>The shapes below are also congruent. It’s just that they are not facing the same way. </li></ul>Congruence
  44. 44. <ul><li>Two shapes are similar if the are the same shape but not the same size. </li></ul>Similarity These two shapes are similar because they are the same shape, but one is smaller. These two shapes are not similar because they even though they are both rectangles, they are not the same shape.
  45. 45. <ul><li>Think about this - all circles and squares are either congruent or similar. </li></ul>Similarity
  46. 46. Transformations <ul><li>Transformations are ways of moving shapes. The three we learned are: </li></ul><ul><li>flips </li></ul><ul><li>slides </li></ul><ul><li>turns </li></ul>
  47. 47. Transformations The thing to remember about tranformations is this: they don't change the size or shape of the original polygon
  48. 48. <ul><li>A flip is like a reflection. A shape flips over itself. </li></ul>Transformations These are both flips .
  49. 49. <ul><li>A shape is turned when it rotates around a corner. </li></ul>Transformations These are all turns .
  50. 50. <ul><li>Sliding means moving in any direction without turning it or flipping it. These are all slides . </li></ul>Transformations
  51. 51. <ul><li>When shapes tessellate, they fit together perfectly to cover a page. For example, hexagons tessellate nicely . </li></ul>Tessellations
  52. 52. <ul><li>But lots of other shapes tessellate as well . In fact, there are artists who specialize in creating tessellations. One of the most famous is M.C. Escher. Below is one of his works. </li></ul>Tessellations Pictures courtesy of: www.tessellations.org/eschergallery10.htm
  53. 53. <ul><li>You don’t have to be an artist to make a tessellation. Just click on the picture below to find directions for making your own. Good luck! </li></ul>Tessellations
  54. 54. <ul><li>Below are some websites where you can view some tessellations and learn more about them. </li></ul>Tessellations http://tessellations.org/ http://library.thinkquest.org/16661/mosaics.html
  55. 55. Some Helpful Websites http://www.mathleague.com/help/geometry/polygons.htm http://www.mathsisfun.com/geometry/index.html
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