Transcript Three-dimensional Shapes (3D)

Three-dimensional Shapes (3D)
• These shapes are
solid or hollow, you
could hold them in
your hand.
• They have three
dimensions: length,
width and height.
Solid
• A shape you can
hold (3D).
• A solid has
length, width and
height.
• Examples:
–
–
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–
–
Cube
Cylinder
Sphere
Cone
Prism
Surface
• The curved part of a
3D shape.
• Cylinders and cones
have surfaces.
Face
• Part of a 3D shape
that is flat.
• Example: A cube has
6 faces.
Base
• The bottom
face of a 3D
object.
Base
Edge
• The line where two
faces meet on a 3D
object.
• Example: A cube has
12 edges.
Corner
• The point where three
or more edges touch.
• This cube has 12
corners all together.
Vertex (Vertices)
• The point where three
or more edges meet.
• This cube has 12
vertices all together.
Cube
• A 3D shape (you can
hold it).
• It has 6 equal square
faces.
• Cubes in daily life:
– A box
– Blocks
– Dice
Cube
• A three-dimensional
shape which has:
– 6 square faces all the
same size
– 12 edges
– 8 corners
Cube
• A three-dimensional
shape which has:
– 6 square faces all the
same size
– 12 edges
– 8 vertices
Cube
• A three-dimensional
shape which has 6
square faces all the
same size, 12 edges
and 8 vertices.
• Some faces parallel
• Some edges parallel
• Some faces
perpendicular
• Some edges
perpendicular
Sphere
• A 3D shape (you can
hold it) that can roll.
• A Sphere has no
corners or edges
• Spheres in daily life:
– A Ball
– A Globe
– A Marble
Sphere
• A perfectly round
three-dimensional
shape, like a ball. It
has only one curved
surface.
• A sphere has
– 0 faces
– 0 edges
– 0 corners
Sphere
• A perfectly round
three-dimensional
shape, like a ball. It
has only one curved
surface.
• A sphere has
– 0 faces
– 0 edges
– 0 vertices
Cone
• A 3D shape (you can
hold it) that can roll.
• A Cone has a circle at
its base and a curved
surface that comes to
a point at its top
(vertex).
• Cones in daily life:
– Ice Cream Cone
– A Party Hat
Cone
• A three-dimensional
shape made up of:
– a circular base
– a curved surface that
comes to a point at the
top (vertex).
• A Cone has 0 edges
and 0 corners.
Cone
• A three-dimensional
shape made up of:
– a circular base
– a curved surface that
comes to a point at the
top (vertex).
• A Cone has 0 edges
and 0 vertices.
Cylinder
• A 3D shape (you can
hold it) that can roll.
• A Cylinder has 2
equal circles on its
ends.
• Cylinders in daily life:
– A Soup Can
– A Roll of Toilet Paper
Cylinder
• A three-dimensional
shape with one
curved surface and 2
equal circles on its
ends.
• A Cylinder has 2
faces, 1 surface, 0
edges and
0 corners.
Cylinder
• A three-dimensional
shape with one
curved surface and 2
equal circles on its
ends.
• A Cylinder has 2
faces, 1 surface, 0
edges and
0 vertices.
Pyramid
• A three-dimensional
shape which has a
polygon for its base
and triangular faces
which meet at one
point (vertex).
Rectangular Prism
• A 3D shape (you can
hold it).
• It has 6 rectangular
faces.
• Cubes in daily life:
– A Kleenex Box
– A Refrigerator
– A Cereal Box
Rectangular Prism
• A 3D shape that has:
– 6 rectangular faces
• 2 of those faces are
equal
– 12 edges
– 8 corners
Rectangular Prism
• A 3D shape that has:
– 6 rectangular faces
• 2 of those faces are
equal
– 12 edges
– 8 vertices
Rectangular Prism
• A 3D shape that has:
– 6 rectangular faces
• 2 of those faces are
equal
– 12 edges
– 8 vertices
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Some faces are parallel
Some edges are parallel
Some faces are perpendicular
Some edges are perpendicular
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.
Sides
• The lines you can
trace and count
on the outside of
a 2D shape.
• Example: A
triangle has 3
sides. A square
has 4.
Polygons
• Two-dimensional
shapes that have
three or more sides
made from straight
lines.
• Examples:
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triangles
squares
rectangles
Quadrilaterals
• Any twodimensional shapes
(polygon) with 4
straight sides and 4
angles
• Ex.
rhombus
rectangle
square
kite
trapezoid
Quadrilaterals
• Any twodimensional shapes
(polygon) with 4
straight sides and 4
angles
• The interior angles
of a Quadrilateral
add up to 360
degrees.
• Ex.
rhombus
rectangle
square
kite
trapezoid
Parallelogram
• A quadrilateral with
parallel opposite
sides of equal
length.
• Opposite angles are
equal.
Rectangle
• A 2D shape with 4
corners and 2 pairs of
opposite, equal,
parallel sides.
• Rectangles in daily
life:
– A Door
– A Piece of Paper
Rectangle
• A 2D shape with 4
corners and 2 pairs of
opposite, equal,
parallel sides.
• The sides meet at
right angles.
Rhombus
• A 2D shape with four
sides.
Rhombus
• A 2D, four-sided
shape with opposite
sides that are parallel.
• All the sides are the
same length.
Rhombus
• A 2D, four-sided
shape with opposite
sides that are parallel.
• All the sides are the
same length.
• Diagonals of a
Rhombus bisect each
other at right angles.
Trapezoid
• A 2D shape (polygon)
with four sides.
• One pair of sides is
parallel.
Trapezoid
• A 2D shape (polygon)
with four sides.
• One pair of sides is
parallel.
Circle
• A 2D shape with no
corners or edges.
• Circles in daily life:
– A Clock
Semicircle
• A 2D shape that is
exactly half of a
circle.
• Semicircles in daily
life:
– Half of a pie
– Half of a pizza
Square
• 2D shape with 4
equal sides and 4
corners
• Squares in daily life:
– A Window
– Some Floor Tiles
– Some Ceiling Tiles
Square
• 2D shape (polygon)
with 4 equal sides
and 4 right (90°)
angles.
• Opposite sides are
parallel.
Triangle
• Two-dimensional
shape with three
straight sides and
three corners.
• Triangles in daily life:
– The front of a tent
Triangle
• Two-dimensional
shape (polygon) with
three straight sides
and three angles.
• There are
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isosceles triangles,
right triangles
equilateral triangles
scalene triangles
Triangle
• Two-dimensional
shape (polygon)
with three straight
sides and three
angles.
• The interior angles
of a triangle add up
to 180 degrees.
• There are
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isosceles triangles,
right triangles
equilateral triangles
scalene triangles
Patterns
• A repeating design.
Examples:
AB
AA B
Growing
Line
• A long, thin
mark that
continues
forever.
• It has no
endpoints.
Line
• An infinitely
long, thin, twodimensional
mark
• It has no
endpoints.
Parallel
• Lines that are the
same distance apart
from each other.
• These type of lines
stay the same
distance apart for
their whole length.
They do not need to
be straight or the
same length.
• They never intersect.
Perpendicular
• Lines that intersect at
a perfect right angle
(90º) to one another.
• In solid shapes,
edges could be at a
right angle to one
another.
• Faces could also be
at right angles to one
another.
Intersecting
• Crossing over one
another.
• These lines are
intersecting.
Line Segment
• A section of line
bounded by two
endpoints.
• A line segment
is not
continuous.
Point
• A single position
in space (dot).
Distance
A
B
• The length
between two
points or
objects.
Angles
• A shape formed
by two lines or
rays that extend
from a common
point (vertex).
• The amount of
turning between
two lines that
meet at a
common point
(vertex).
Vertex (angles)
• The common
point between
two or more
rays or line
segments.
Acute Angle
• An angle that
measures less
than 90 degrees.
Right Angle
• An angle whose
measure is
exactly 90
degrees.
Obtuse Angle
• An angle whose
measure is more
than 90 degrees.
Straight Angle
• An angle whose
measure is
exactly 180
degrees.
• A straight line.
Interior Angles
• Any angle
inside a
polygon.
Congruent
• Two figures are
congruent if they
have the same
shape and size.
• Two angles are
congruent if they
have the same
measure.
Vertical Angles
• A pair of angles
directly opposite
each other
formed by the
intersection of
straight lines.
• Vertical angels
are congruent
(equal).
Isosceles Triangle
• A triangle with
2 equal sides
and 2 equal
angles
Equilateral Triangle
• A triangle with
3 equal sides and
3 equal angles.
Right Triangle
• A triangle with one
right angle (90
degrees).
Scalene Triangles
• A triangle with 3
different side
lengths and 3
different angle
measures.
Symmetry
• An object is
symmetrical
when you can
fold it in half and
the two halves
are congruent.
• One half is a
mirror image of
the other.
Symmetrical
Not Symmetrical