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Geometry Review

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mrsfoster

The document provides an overview of various geometry concepts including: - Solid shapes such as cubes, cylinders, and cones and their defining characteristics - Lines, angles, and their classifications - Circles and their components such as diameters and radii - Polygons defined by their number of sides - Properties of triangles, quadrilaterals, and other shapes - Symmetry, congruence, transformations, and tessellations

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Geometry Review
Solid Shapes Solid shapes have three parts: faces, edges, and vertices. Look at the shape below to see what each is. face vertex edge Note: Faces must be flat!
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 - goes on in both directions forever ray - has one endpoint, goes on in one way forever
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
Lines and Angles There are 3 ways lines can be related: parallel intersecting perpendicular parellel - never intersect intersecting - cross at a point perpendicular - intersect and form right angles
Circles 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.
Circles The name of this circle is B. B
Circles This is a radius . It is named AB or BA . B A
Circles Below is the diameter of the circle. It is named CD or DC . B C D
Circles A diameter is made up of two radii. So to find the length of the diameter, you just double the length of a radius. B C D 2” If the length of the radius is 2 inches, the length of the diameter is 4 inches.
Polygons A polygon is a closed figure with straight sides . The are classified by the number of sides they have. 3 sides – triangle 4 sides – quadrilateral 5 sides – pentagon 6 sides – hexagon 8 sides - octagon 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.
These are all triangles because they have 3 sides. Polygons
How many triangles are in this picture ? Polygons
These are all quadrilaterals because they have 4 sides . Polygons
These are all pentagons because they have 5 sides. Polygons
These are all hexagons because they have 6 sides. Polygons
These are all octagons because they have 8 sides. Polygons
Triangles Triangles are classified in two ways: by the length of their sides, and by their angles. Sides Equilateral – all 3 sides the same Isosceles – 2 sides the same Scalene – no side the same Angles Right – one right angle Obtuse – one obtuse angle Acute – all three angles acute
These are all right triangles because they each have one right angle. Triangles
These are all acute triangles because all of the angles are acute. Triangles
These are all obtuse triangles because the have one obtuse angle. Triangles
These are all equilateral triangles because all 3 sides are congruent. Triangles
These are all isosceles triangles because they have 2 congruent sides. Triangles
These are all scalene triangles because none of the sides are congruent. Triangles
Quadrilaterals Quadrilateral are 4-sided figures. Some special quadriltaterals are: Square- 4 sides the same; 4 right angles; 2 sets parallel sides Rectangle – 4 right angles; 2 sets parallel sides Parallelogram – 2 sets parallel sides Rhombus – 2 sets parallel sides; 4 sides the same Trapezoid – 1 set parallel sides
quadrilateral trapezoid parallelogram rhombus rectangle square square
Quadrilaterals Image found at: www.cimt.plymouth.ac.uk/.../bk8i15/bk8_15i4.htm
These are all rhombii (the plural of rhombus) because they have: 2 sets of parallel sides 4 congruent sides Quadrilaterals
These are all squares because they have: 2 sets of parallel sides 4 congruent sides 4 right angles Quadrilaterals
These are all trapezoids because they all have: 1 set of parallel sides Quadrilaterals
These are all rectangles because they all have: 2 sets of parallel sides 2 sets of congruent sides 4 right angles Quadrilaterals
These are all parallelograms because they all have: 2 sets of parallel sides 2 sets of congruent sides Quadrilaterals
Symmetry This shape has symmetry. This shape does not. 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.
The shape below does not have a line of symmetry. Symmetry
The shape below has two lines of symmetry. Symmetry
Congruence Shapes are congruent if the are same size and shape. These two shapes are congruent. These two shapes are not.
The shapes below are also congruent. It’s just that they are not facing the same way. Congruence
Two shapes are similar if the are the same shape but not the same size. 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.
Think about this - all circles and squares are either congruent or similar. Similarity
Transformations Transformations are ways of moving shapes. The three we learned are: flips slides turns
Transformations The thing to remember about tranformations is this: they don't change the size or shape of the original polygon
A flip is like a reflection. A shape flips over itself. Transformations These are both flips .
A shape is turned when it rotates around a corner. Transformations These are all turns .
Sliding means moving in any direction without turning it or flipping it. These are all slides . Transformations
When shapes tessellate, they fit together perfectly to cover a page. For example, hexagons tessellate nicely . Tessellations
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. Tessellations Pictures courtesy of: www.tessellations.org/eschergallery10.htm
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! Tessellations
Below are some websites where you can view some tessellations and learn more about them. Tessellations http://tessellations.org/ http://library.thinkquest.org/16661/mosaics.html
Some Helpful Websites http://www.mathleague.com/help/geometry/polygons.htm http://www.mathsisfun.com/geometry/index.html

More Related Content

Geometry Review

  • 2. Solid Shapes Solid shapes have three parts: faces, edges, and vertices. Look at the shape below to see what each is. face vertex edge Note: Faces must be flat!
  • 3. Solid Shapes A cylinder has 2 faces and 2 edges. edge face
  • 4. Solid Shapes A cube has 6 faces, 12 edges and 8 vertices. face vertex edge
  • 5. Solid Shapes A cone has 1 face, 1 vertex and 1 edge. face edge face(on bottom)
  • 6. Solid Shapes A square pyramid has 5 faces, 8 edges, and 5 vertices. face vertex edge
  • 7. Solid Shapes A sphere has no faces, edges, or vertices, but we love it anyway!
  • 8. Solid Shapes A rectangular prism has 6 faces, 12 edges, and 8 vertices, just like a square. face edge vertex
  • 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. 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. Lines and Angles There are 3 ways lines can be related: parallel intersecting perpendicular parellel - never intersect intersecting - cross at a point perpendicular - intersect and form right angles
  • 12. Circles 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.
  • 13. Circles The name of this circle is B. B
  • 14. Circles This is a radius . It is named AB or BA . B A
  • 15. Circles Below is the diameter of the circle. It is named CD or DC . B C D
  • 16. Circles A diameter is made up of two radii. So to find the length of the diameter, you just double the length of a radius. B C D 2” If the length of the radius is 2 inches, the length of the diameter is 4 inches.
  • 17. Polygons A polygon is a closed figure with straight sides . The are classified by the number of sides they have. 3 sides – triangle 4 sides – quadrilateral 5 sides – pentagon 6 sides – hexagon 8 sides - octagon 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. These are all triangles because they have 3 sides. Polygons
  • 19. How many triangles are in this picture ? Polygons
  • 20. These are all quadrilaterals because they have 4 sides . Polygons
  • 21. These are all pentagons because they have 5 sides. Polygons
  • 22. These are all hexagons because they have 6 sides. Polygons
  • 23. These are all octagons because they have 8 sides. Polygons
  • 24. Triangles Triangles are classified in two ways: by the length of their sides, and by their angles. Sides Equilateral – all 3 sides the same Isosceles – 2 sides the same Scalene – no side the same Angles Right – one right angle Obtuse – one obtuse angle Acute – all three angles acute
  • 25. These are all right triangles because they each have one right angle. Triangles
  • 26. These are all acute triangles because all of the angles are acute. Triangles
  • 27. These are all obtuse triangles because the have one obtuse angle. Triangles
  • 28. These are all equilateral triangles because all 3 sides are congruent. Triangles
  • 29. These are all isosceles triangles because they have 2 congruent sides. Triangles
  • 30. These are all scalene triangles because none of the sides are congruent. Triangles
  • 31. Quadrilaterals Quadrilateral are 4-sided figures. Some special quadriltaterals are: Square- 4 sides the same; 4 right angles; 2 sets parallel sides Rectangle – 4 right angles; 2 sets parallel sides Parallelogram – 2 sets parallel sides Rhombus – 2 sets parallel sides; 4 sides the same Trapezoid – 1 set parallel sides
  • 32. quadrilateral trapezoid parallelogram rhombus rectangle square square
  • 33. Quadrilaterals Image found at: www.cimt.plymouth.ac.uk/.../bk8i15/bk8_15i4.htm
  • 34. These are all rhombii (the plural of rhombus) because they have: 2 sets of parallel sides 4 congruent sides Quadrilaterals
  • 35. These are all squares because they have: 2 sets of parallel sides 4 congruent sides 4 right angles Quadrilaterals
  • 36. These are all trapezoids because they all have: 1 set of parallel sides Quadrilaterals
  • 37. These are all rectangles because they all have: 2 sets of parallel sides 2 sets of congruent sides 4 right angles Quadrilaterals
  • 38. These are all parallelograms because they all have: 2 sets of parallel sides 2 sets of congruent sides Quadrilaterals
  • 39. Symmetry This shape has symmetry. This shape does not. 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. The shape below does not have a line of symmetry. Symmetry
  • 41. The shape below has two lines of symmetry. Symmetry
  • 42. Congruence Shapes are congruent if the are same size and shape. These two shapes are congruent. These two shapes are not.
  • 43. The shapes below are also congruent. It’s just that they are not facing the same way. Congruence
  • 44. Two shapes are similar if the are the same shape but not the same size. 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. Think about this - all circles and squares are either congruent or similar. Similarity
  • 46. Transformations Transformations are ways of moving shapes. The three we learned are: flips slides turns
  • 47. Transformations The thing to remember about tranformations is this: they don't change the size or shape of the original polygon
  • 48. A flip is like a reflection. A shape flips over itself. Transformations These are both flips .
  • 49. A shape is turned when it rotates around a corner. Transformations These are all turns .
  • 50. Sliding means moving in any direction without turning it or flipping it. These are all slides . Transformations
  • 51. When shapes tessellate, they fit together perfectly to cover a page. For example, hexagons tessellate nicely . Tessellations
  • 52. 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. Tessellations Pictures courtesy of: www.tessellations.org/eschergallery10.htm
  • 53. 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! Tessellations
  • 54. Below are some websites where you can view some tessellations and learn more about them. Tessellations http://tessellations.org/ http://library.thinkquest.org/16661/mosaics.html
  • 55. Some Helpful Websites http://www.mathleague.com/help/geometry/polygons.htm http://www.mathsisfun.com/geometry/index.html