Two- and Three-Dimensional Figures Advanced Geometry Inductive Reasoning Lesson 3 Two- and Three-Dimensional Figures

Polygon Named by: all vertices written in consecutive order Examples NO HOLES NO CURVES SIDES CANNOT OVERLAP Named by: all vertices written in consecutive order

Convex Concave “caves in” extend the sides extend the sides all extensions lie outside the figure any extension crosses inside the figure

Names of Polygons triangle quadrilateral pentagon hexagon heptagon # of sides and angles Name of Polygon 3 4 5 6 7 8 9 10 n triangle quadrilateral pentagon hexagon heptagon octagon nonagon decagon n - gon

Regular Polygon convex polygon all the sides are congruent and all angles are congruent

Examples: Name each polygon by its number of sides Examples: Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular. Pentagon convex regular

Perimeter and Area of a Rectangle Area – the number of square units needed to cover a surface Perimeter – the sum of the lengths of the sides of a polygon ADD ALL SIDES

Circumference and Area of a Circle Circumference – the distance around a circle Area

Example: Mr. Smith has a circular fence that encloses an area with a diameter of 12 feet. Using the same fence, he wants to create a square fence. What is the maximum side length of the square?

Example: Find the perimeter of a square with an area of 30 square centimeters.

Example: Find the circumference of a circle with an area of 36 square units.

Example: Find the length of each side of the polygon below if its perimeter is 20 units.

Polyhedron Definition: a solid with all flat surfaces that enclose a single region of space All flat surfaces are called faces. The line segments where the faces intersect are edges. The points where the edges intersect are vertices.

Prisms The two bases are parallel AND congruent. Named by: the shape of the bases Triangular Prism Rectangular Prism Pentagonal Prism A regular prism has bases that are regular polygons.

Pyramids one base Named for: the base Triangular Pyramid Rectangular Hexagonal Pyramid

This picture is on page 62 in your textbook. Examples: Identify each solid. Name the bases, faces, edges, and vertices. Bases – Faces – Edges – Vertices – This picture is on page 62 in your textbook.

This picture is on page 61 in your textbook. Examples: Identify each solid. Name the bases, faces, edges, and vertices. Bases – Faces – Edges – Vertices – This picture is on page 61 in your textbook.

NOT polyhedra (polyhedrons) Cylinders Cones Spheres The two bases are congruent, parallel circles. one circular base NOT polyhedra (polyhedrons)

This picture is on page 62 in your textbook. Examples: Identify each solid. Name the bases, faces, edges, and vertices. Bases – Faces – Edges – Vertices – This picture is on page 62 in your textbook.

This picture is on page 61 in your textbook. Examples: Identify each solid. Name the bases, faces, edges, and vertices. Bases – Faces – Edges – Vertices – This picture is on page 61 in your textbook.

Height vs. Slant Height

Surface Area and Volume Prisms Pyramids

Surface Area and Volume Cylinders Cones

Examples: Find the surface area and volume of the square prism.

This picture is on page 62 in your textbook. Examples: Find the surface area and volume of the square pyramid. This picture is on page 62 in your textbook.

Examples: Find the surface area and volume of the square pyramid.