Download 2D & 3D Geometric Shapes

2D & 3D Geometric
Shapes
Characteristics
&
Properties
Polygon


A simple, closed, twodimensional figure formed by
three or more sides.
When all of the sides and all of
the angles are congruent, the
polygon is a regular polygon.
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Number of
Sides
3
4
5
6
7
8
9
Scalene Triangle


No sides congruent
No two angles are equal in measure
either.
Isosceles Triangle

At least two sides congruent.
Equilateral Triangle


All sides congruent
All angles congruent
Acute Triangle
All of the angles are less than 90º.
Right Triangle
Has at least one 90º angle.
Obtuse Triangle
Has one angle that is greater than
90º.
Squares & Rhombuses






All sides congruent
Square: All angles are right angles
Rhombus: Opposite angles are
congruent
Opposite sides are parallel
Each diagonal of a rhombus bisects
two angles of the rhombus
The diagonals are perpendicular and
congruent
Rectangles & Parallelograms





Opposite sides congruent
Rectangle: All angles are right angles
Parallelogram: Opposite angles are
congruent
Opposite sides are parallel
The diagonals of a parallelogram
bisect each other
Trapezoid



Bases are parallel.
The base angles of an isosceles
trapezoid are congruent
The diagonals of an isosceles
trapezoid are congruent
Kite




Two pairs of adjacent sides
The adjacent sides are congruent
Opposite sides are not congruent
The diagonals of a kite are congruent
Polyhedron




A three-dimensional figure whose
surfaces are polygons.
Each polygon is a face of the
polyhedron.
An edge is a segment that is formed
by the intersection of two faces.
A vertex is a point where three or
more edges intersect.
Three dimensional shapes





Have length, width, and depth.
Terms associated with them are face,
edge, vertex, and lateral face.
The flat surfaces are faces.
The base is the bottom.
The lateral faces are those faces that
are not bases.
Polyhedron cont.

A net is a two-dimensional pattern
that you can fold to form a threedimensional figure.
Prism



Has at least three lateral faces that
are rectangles.
The top and bottom are bases and
are parallel.
The shape of the base tells the name
of the prism.
Pyramids



Has at least 3 lateral faces that are
triangles and only one base.
The base can be shaped like any
closed figure with three or more
sides.
The shape of the base tells the name
of the pyramid.
Cone



Has only one base which is a circle.
Has one curved surface.
Has one vertex and no edges.
Cylinder



Has only 2 bases which are circles.
These 2 circles are parallel and
congruent.
The bases are connected by a curved
side.
Has no vertices and no edges.
Sphere



All of the points on a sphere are the
same distance from the center.
All spheres are similar.
No faces, bases, edges, or vertices.
Surface Area


Surface Area (SA) is the sum of the
lateral area and the area of the two
bases.
Lateral Area is the sum of the areas
of the lateral faces.
Surface Area of a Prism




SA=2lw+2lh+2hw
w=width
l=length
h=height
Surface Area of a Cylinder
SA=2∏rh+2∏r¹
Volume
Volume of a Prism
V=lwh