Geometry and Spatial Sense

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Geometry and Spatial Sense

• Properties of 2-D and 3-D Shapes

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ObjectiveTo identify and classify
two-dimensional (2-D) shapes by side and angle
properties such as perpendicular and parallel
lines, faces and edges, and compare and sort
three-dimensional (3-D) figures
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PART 1SOLID SHAPES
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Two-dimensional Shapes (2D)

• These shapes are flat and can only be drawn on
  paper.
• They have two dimensions length and width.
• They are sometimes called plane shapes.

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Three-dimensional Shapes (3D)

• These shapes are solid or hollow.
• They have three dimensions length, width and
  height.

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Face

• Part of a shape that is flat or curved.
• E.g. A cube has 6
• of these.

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Edge

• The line where two faces meet.
• E.g. A cube has 12 of these.

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Vertex (Vertices)

• The place where three or more edges meet.
• This pyramid has 4 of these.

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Parallel

• These type of lines stay the same distance apart
  for their whole length. They do not need to be
  straight or the same length.

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Perpendicular

• A line that is drawn in a right angle to another
  line .
• In solid shapes edges could be at a right angle
  to one another.
• Faces could also be at right angles to one
  another.

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Cube

• A three-dimensional shape which has 6 square
  faces all the same size.

Some faces parallel Some edges parallel
Some faces perpendicular Some edges perpendicular
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Cuboid

• A three-dimensional shape which has 6 rectangular
  faces.

Some faces parallel Some edges parallel
Some faces perpendicular Some edges perpendicular
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Sphere

• A perfectly round three-dimensional shape, like a
  ball. It has only one curved face.

No parallel faces or edges
No perpendicular faces or edges
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Hemisphere

• A three-dimensional shape that is half a sphere.

No parallel faces or edges
No perpendicular faces or edges
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Cone

• A three dimensional shape with a circle at its
  base and a pointed vertex.

No parallel faces or edges
No perpendicular faces or edges
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Cylinder

• A three-dimensional shape with circular ends of
  equal size.

Some faces parallel Some edges parallel
Some faces perpendicular No edges perpendicular
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Pyramid

• A three-dimensional shape which has a regular
  polygon for its base and triangular faces which
  meet at one vertex.

• E.g. Triangular pyramid
• Square pyramid
• Hexagonal pyramid
• Pentagonal pyramid

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Square base pyramid
No faces parallel Some edges parallel
No faces perpendicular Some edges perpendicular
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On Your Own

• Using the printout of the different shapes I have
  handed out, please classify cone, cylinder,
  square-based pyramid, cube, cuboid, sphere, and
  hemisphere into the charts on the handout titled
  Properties 3-D Shapes
• Note There may not be a shape in all of the
  boxes!!!
• What do you notice about the shapes you were able
  to put in the cells? There is one thing they all
  have in common.
• I will show you the answers on the next slide
  when you are done.

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Written Task - Faces
SOME PARALLEL FACES
NO PARALLEL FACES
Cube Cuboid Cylinder
SOME PERPENDICULAR FACES
Cone Square based- Pyramid Sphere Hemispere
NO PERPENDICULAR FACES
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Written Task - Edges
SOME PARALLEL EDGES
NO PARALLEL EDGES
Cube Cuboid Square-based pyramid
SOME PERPENDICULAR EDGES
Sphere Hemisphere Cone
Cylinder
NO PERPENDICULAR EDGES
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PART 2PLANE SHAPES
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Polygons

• Two-dimensional shapes that have sides made from
  straight lines.
• E.g. triangles
• squares
• hexagons

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Quadrilaterals

• Any two-dimensional shapes with four straight
  sides.
• E.g. square
• rhombus
• rectangle
• trapezium
• kite

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Rectangle

• A four sided two-dimensional shape with two pairs
  of parallel sides that meet at right angles.

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Kite

• A two-dimensional shape with two shorter sides of
  equal length and two longer sides of equal
  length.

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Rhombus

• A two-dimensional four sided shape with opposite
  sides that are parallel and all the sides are the
  same length.

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Trapezoid

• A two-dimensional shape with four sides.One pair
  of sides is parallel with one side longer than
  the other.

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Pentagon

• A two-dimensional shape with five straight sides
  and five angles.

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Hexagon

• A two-dimensional shape with 6 straight sides and
  6 angles.

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Octagon

• A two-dimensional shape with 8 straight sides and
  8 angles.

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What do we call a shape with7 Sides?9
Sides?10 Sides?
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Circle

• A round flat two-dimensional shape.

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Square

• Two dimensional shape with 4 sides of the same
  length and 4 90 angles.

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Triangle

• Two-dimensional shape with three straight sides
  and three angles.