2D & 3D Geometric Shapes Characteristics&Properties

Polygon A simple, closed, two- dimensional figure formed by three or more sides. A simple, closed, two- dimensional 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. When all of the sides and all of the angles are congruent, the polygon is a regular polygon.

9Nonagon 8Octagon 7Heptagon 6Hexagon 5Pentagon 4Quadrilateral 3Triangle Number of Sides Polygon

Scalene Triangle No sides congruent No sides congruent No two angles are equal in measure either. No two angles are equal in measure either.

Isosceles Triangle At least two sides congruent. At least two sides congruent.

Equilateral Triangle All sides congruent All sides congruent All angles 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 All sides congruent Square: All angles are right angles Square: All angles are right angles Rhombus: Opposite angles are congruent Rhombus: Opposite angles are congruent Opposite sides are parallel Opposite sides are parallel Each diagonal of a rhombus bisects two angles of the rhombus Each diagonal of a rhombus bisects two angles of the rhombus The diagonals are perpendicular and congruent The diagonals are perpendicular and congruent

Rectangles & Parallelograms Opposite sides congruent Opposite sides congruent Rectangle: All angles are right angles Rectangle: All angles are right angles Parallelogram: Opposite angles are congruent Parallelogram: Opposite angles are congruent Opposite sides are parallel Opposite sides are parallel The diagonals of a parallelogram bisect each other The diagonals of a parallelogram bisect each other

Trapezoid Bases are parallel. Bases are parallel. The base angles of an isosceles trapezoid are congruent The base angles of an isosceles trapezoid are congruent The diagonals of an isosceles trapezoid are congruent The diagonals of an isosceles trapezoid are congruent

Kite Two pairs of adjacent sides Two pairs of adjacent sides The adjacent sides are congruent The adjacent sides are congruent Opposite sides are not congruent Opposite sides are not congruent The diagonals of a kite are congruent The diagonals of a kite are congruent

Polyhedron A three-dimensional figure whose surfaces are polygons. A three-dimensional figure whose surfaces are polygons. Each polygon is a face of the polyhedron. Each polygon is a face of the polyhedron. An edge is a segment that is formed by the intersection of two faces. 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. A vertex is a point where three or more edges intersect.

Three dimensional shapes Have length, width, and depth. Have length, width, and depth. Terms associated with them are face, edge, vertex, and lateral face. Terms associated with them are face, edge, vertex, and lateral face. The flat surfaces are faces. The flat surfaces are faces. The base is the bottom. The base is the bottom. The lateral faces are those faces that are not bases. 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 three- dimensional figure. A net is a two-dimensional pattern that you can fold to form a three- dimensional figure.

Prism Has at least three lateral faces that are rectangles. Has at least three lateral faces that are rectangles. The top and bottom are bases and are parallel. The top and bottom are bases and are parallel. The shape of the base tells the name of the prism. 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. 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 base can be shaped like any closed figure with three or more sides. The shape of the base tells the name of the pyramid. The shape of the base tells the name of the pyramid.

Cone Has only one base which is a circle. Has only one base which is a circle. Has one curved surface. Has one curved surface. Has one vertex and no edges. Has one vertex and no edges.

Cylinder Has only 2 bases which are circles. These 2 circles are parallel and congruent. Has only 2 bases which are circles. These 2 circles are parallel and congruent. The bases are connected by a curved side. The bases are connected by a curved side. Has no vertices and no edges. Has no vertices and no edges.

Sphere All of the points on a sphere are the same distance from the center. All of the points on a sphere are the same distance from the center. All spheres are similar. All spheres are similar. No faces, bases, edges, or vertices. 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. 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. Lateral Area is the sum of the areas of the lateral faces.

Surface Area of a Prism SA=2lw+2lh+2hw SA=2lw+2lh+2hw w=width w=width l=length l=length h=height h=height

Surface Area of a Cylinder SA=2∏rh+2∏r¹

Volume

Volume of a Prism V=lwh