Section 12-1 Name the Solids

Prism a 3-dimensional figure with two congruent, parallel faces The bases are congruent, parallel faces. The bases lie in parallel planes.

Base

Altitude of a prism perpendicular distance (a segment) between its bases. The length of the altitude is the height of the prism!

altitude

the faces that are not its bases In the shape of parallelograms Lateral faces of a prism

the parallel segments where adjacent lateral faces intersect Lateral Edges

Types of prisms 1.Right Prism: –h–have rectangles for the lateral faces –L–Lateral edges are altitudes 2.Oblique prism: –L–Lateral edges are NOT altitudes

Example of a Right Prism: Example of an Oblique Prism: Height

A prism is named by the shape of its base.

Some Examples of Right Prisms: Rectangular Prism: Base

A rectangular prism whose edges have equal length. Cube

Triangular Prism: : Pentagonal Prism Base

Hexagonal Prism: And the list goes on….. Base

pyramid Has only one base, which is a polygon, and for lateral faces triangles with a common vertex Base Vertex

The lateral faces intersect in segments called lateral edges.

Altitude of a pyramid The segment from the vertex perpendicular to the base The length of the altitude is the height of the pyramid!

altitude

A pyramid is named by the shape of its base.

Examples Triangular Pyramid Square Pyramid Pentagonal Pyramid Hexagonal Pyramid

Properties of Regular pyramids 1.The base is a regular polygon. 2.All lateral edges are congruent. 3.All lateral faces are congruent isosceles triangles. 4.The height of a lateral face is called the slant height ( l ) of the pyramid. 5.The altitude meets the base at its center.

Other 3- Dimensional figures have curved faces

cylinder A solid with congruent circular bases that lie in parallel planes Bases

The altitude is the perpendicular distance between its bases. Parts of a Cylinder

The length of the altitude is called the height. A radius of a base is the radius of the cylinder. r h

cone Has a circular base and vertex that is not in the same plane as the base.

The altitude (height) is the perpendicular distance between the vertex and the base. The slant height is the distance between the vertex and a point on the base edge.

Base Vertex height Slant height

sphere Set of all points in space at a given distance from a given point, called the center.

Many of the terms used with circles are used with spheres:

Great circle The intersection of a plane and a sphere so that the center of a sphere is included

hemisphere Two congruent halves of a sphere separated by a great circle.

net A two dimensional pattern that when folded forms a three dimensional figure. Dotted lines indicate folds.

Example of a Net