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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:
– 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.
BaseBase
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
• 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:– triangles– squares– rectangles
Quadrilaterals• Any two-dimensional
shapes (polygon) with 4 straight sides and 4 angles
• Ex.
rhombus kite
rectangle trapezoid
square
Quadrilaterals• Any two-dimensional
shapes (polygon) with 4 straight sides and 4 angles
• The interior angles of a Quadrilateral add up to 360 degrees.
• Ex. rhombus kite rectangle trapezoid
square
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 – 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 – isosceles triangles,– right triangles– equilateral triangles– scalene triangles
Patterns• A repeating design.
Examples:Examples:
A BA B
A A BA A B
GrowingGrowing
Line• A long, thin
mark that continues forever.
• It has no endpoints.
Line• An infinitely
long, thin, two-dimensional 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• The length
between two points or objects.
AA BB
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