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