Lesson 9 8 The Pythagorean Theorem and Space

Lesson 9. 8 The Pythagorean Theorem and Space Figures Objective: After studying this section, you will be able to apply the Pythagorean Theorem to solid figures

Some basic vocabulary you should know! A Polyhedron is a solid formed by polygons that enclose a single region of space. face base A face is the flat polygonal surfaces of the polyhedron In a solid prism there will be a maximum of 2 identical faces called bases.

Words to know continued… A lateral face is the polygonal faces that are not bases. vertex edge Lateral face base An edge is a segment where two faces intersect. A vertex is the point where three or more edges meet.

AG is one of 4 diagonals of the solid A B D D E H Note: A cube is a rectangular solid in which all edges are congruent. F G

A couple more… You name prisms and pyramids by the name of their base. A prism is special type of polyhedron, with 2 faces called bases, that are congruent, parallel polygons. Let’s draw some prisms

Hang in there… A pyramid is special type of polyhedron they have only one base, the other faces are lateral faces that meet to form the lateral edges. The common vertex of the lateral faces is the vertex of the pyramid. Pyramids are classified by their bases Square Pyramid: Triangular Pyramid: Pentagonal Pyramid:

A A is the vertex of the pyramid C D B G E F AB is the altitude of the pyramid and will be perpendicular to the base AE is the slant height and is perpendicular to a side of the base

Example 1 The dimensions of a rectangular solid are 3, 5, and 7. Find the diagonal. A B D D E F H G

Example 2 Given: the regular square pyramid shown with altitude PR and slant height PS, perimeter of JKMO = 40, PK = 13 Find: a. JK b. PS c. PR P O M R J S K

Summary Summarize in your own words the vocabulary that you learned today. Homework: Worksheet 9. 8