Problem of the Day 2-D ShapeArea FormulaLabeled Drawing Rectangle Square Parallelogram Rhombus Triangle Trapezoid

Problem of the Day 2-D ShapeArea FormulaLabeled Drawing RectangleBase height SquareSide side Parallelogram b h Rhombus b h Triangle b h ÷ 2 Trapezoidh(b1 + b2) ÷ 2

8-8: Three-Dimensional Figures

Various 3-D figures

Three Dimensional figures Definition: –Figures that do not lie in a plane –Also called ‘space figures’ or solids Faces –Flat surfaces in 3-D figures –They are shaped like polygons Edge –A segment formed by the intersection of two faces (note: in 2-D we call it a ‘side’)

Three-Dimensional figures

The Great Pyramids of Egypt Source: beersandbeans.com

Pyramids

Definition –Space figures with only one base. –The base is a polygon and other faces are triangles that meet at a vertex. –A pyramid is named for the shape of its base.

Pyramids

Prisms

Definition –A space figure with two parallel and congruent polygonal faces, called bases. The other figures are rectangles (parallelograms). –It is named for the shape of its bases.

Prisms

Polyhedron A three dimensional figure with a polygon for each of its faces is called a polyhedron A polyhedron is a regular polyhedron if all of its faces are regular congruent polygons and all of its edges are congruent.

Skew lines Lines in space that do not intersect and are not parallel are called skew lines

Other space figures or solids There are solids that are not polyhedrons. Some or all of the faces in these types of polyhedrons are not polygons.

Cylinders There are two bases which are parallel and congruent circles Lateral surface Bases

Cones A cone has only one circular base and a vertex. Lateral surface Base

How to distinguish between Prism and Pyramid? Prism If it can stand on both of its bases, it is a prism Pyramid If all the faces come to a point, it is a pyramid

Prisms vs. Pyramids # of bases Shape of other faces? Named after… Pyramid Prism

Prisms vs. Pyramids # of bases Shape of other faces? Named after… PyramidOneTrianglesThe shape of the base PrismTwoRectanglesThe shape of the bases Are all bases considered faces? Are all faces considered bases?

How are prisms and cylinders alike? Each is a space figure with two congruent bases that are parallel and connected by a lateral surface

How are cylinders and cones alike? Each is a space figure with a base that is a circle

How are cylinders and cones different? A cylinder has two bases and a cone has only one base.

Sphere A space figure in the shape of a ball. A set of points that are a given distance from a given point.

Drawing Three-Dimensional Figures 1)Square pyramid 2)Hexagonal prism 3)Your choice – name it and draw it 4)Your choice – name it and draw it 5)Your choice – name it and draw it

Graph Paper

Homework Lesson 8-8, pp. 412 – 413, #s 1–11, 15-25