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.

Slides:

Advertisements

Similar presentations

Chapter 12 – Surface Area and Volume of Solids

Advertisements

Thee-Dimensional Figures and their representations

Chapter 12. Section 12-1  Also called solids  Enclose part of space.

3.4 Polyhedrons and Prisms

Problem of the Day If the figure shown is folded into a cube so that 6 is on the top, what number would be on the bottom? 2.

Surface Areas of Pyramids Unit 5, Lesson 4

10-1 Introduction to Three-Dimensional Figures Warm Up

10-1 Introduction to 3D figs

Geometric Solids A three dimensional figure that has three dimensions: length, width, and height. cylinder Rectangular prism cube pyramid cone.

For This Lesson... You will need: a straightedge.

1-7 Three Dimensional Figures

Prisms Fun with by D. Fisher

Three-Dimensional Figures and Spatial Reasoning

OBJECTIVE AFTER STUDYING THIS SECTION, YOU WILL BE ABLE TO FIND THE SURFACE AREAS OF PRISMS 12.1 Surface Areas of Prisms.

SOLID FIGURES SPI

1 Prisms and Pyramids Mrs. Moy. Lesson 9-2: Prisms & Pyramids 2 Right Prisms Lateral Surface Area (LSA) of a Prism = Ph Total Surface Area (TSA) = Ph.

The Geometry of Solids Section 10.1.

Warm up 1. Any line segment may be extended indefinitely to form a line. 2. Given a line, a circle can be drawn having the segment as a radius and one.

Vertex – A point at which two or more edges meet Edge – A line segment at which two faces intersect Face – A flat surface Vertices, Edges, Faces.

11.3 Surface Areas of Pyramids and Cones A pyramid is a polyhedron in which one face (the base) can be any polygon and the other faces (the lateral faces)

Geometric Solids and Surface Area Geometry Regular Program SY Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson.

The Pyramid Geometric Solids:. Solid Geometry Review: Solid Geometry is the geometry of 3D- dimensional space that we live in. The three dimensions are.

Surface Area, Lateral Area, and Volume of Prisms and Pyramids

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.

Identify each of the following shapes. In geometry, what is a net? what is surface area? cube Triangular pyramid Right square pyramid Rectangular prism.

Warm-Up 1) Draw a polygon that is not convex. 2) Find the measure of an exterior angle of a regular decagon. 3) Find the circumference and area of a circle.

Learn to identify various three-dimensional figures.

8.2 Surface Area Objectives:

Lesson 60 Geometric Solids Prisms & Cylinders. Geometric Solids right triangular prism right circular cylinder regular square pyramid right circular cone.

An introduction to 3D Figures

Polyhedra & Surface Area. Polyhedra Polyhedron – Solid with all flat surfaces that enclose a single region of space. Basically, just a 3D figure whose.

Three Dimensional Figures

Ch 12 and 13 Definitions. 1. polyhedron A solid with all flat surfaces that enclose a single region of space.

Section 9.2 Nack/Jones1 Section 9.2 Pyramids, Area, & Volume.

SURFACE AREA & VOLUME PYRAMIDS Unit 10 April 6, 2015.

Surface area & Volume of Pyramids Tutorial 13d Pyramids §A pyramid is a polyhedron in which one face (the base) can be any polygon and the other faces.

12.5 Surface Areas of Pyramids What you’ll learn: 1.To find lateral areas of regular pyramids. 2.To find surface areas of regular pyramids.

Warm Up Use what you know about 30, 60, 90 triangles to find the missing sides!

1.Square/ Rectangle: A=b x h 2.Triangle: A= ½ b x h ( a triangle is ½ of a rectangle) 3.Circle: A = r2.

PREPARING FOR SURFACE AREA AND VOLUME DRAWINGS, CROSS SECTIONS AND NETS.

9-4 Introduction to Three-Dimensional Figures Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes.

Surface Area and Volume of Pyramids Goal: Students will find the surface area and volume of pyramids.

Lesson 12-2 Pyramids (page 482) Essential Question How is the surface area and volume of pyramids different from prisms?

Warm Up Find the surface area of the right prisms.

12.2 Surface Areas of Pyramids

May look at figures in box to give you some ideas. Geometric Solid:

Section 12-2 Pyramids.

Lesson 9-2: Prisms & Pyramids

9-1 Introduction to Three-Dimensional Figures Warm Up

Preview Warm Up California Standards Lesson Presentation.

INTRODUCTION TO GEOMETRIC SOLIDS.

11.3 Surface Areas of Pyramids and Cones

10.1 Vocab Day 1 Grab a notes page from the back under Geometry on Wednesday Have notebook and homework out.

11.4 Vocabulary Polyhedron Prism, Pyramid, Cylinder, Cone, Sphere

Three-Dimensional Figures and Spatial Reasoning

Lesson 10.3 Three-Dimensional Figures

Lesson 9.8 The Pythagorean Theorem and Space Figures

Warm Up Classify each polygon. 1. a polygon with three congruent sides

10-1 Introduction to Three-Dimensional Figures Warm Up

Three –Dimensional Figures

9-1 Introduction to Three-Dimensional Figures Warm Up

Warm-Up Complete Worksheet

Space Figures & Nets, Surface Areas of Prisms & Cylinders

Geometric Solids All bounded three-dimensional geometric figures. Examples: Sphere, Cylinders, Cubes, Cones, Pyramids, and Prisms.

Geometric Solids All bounded three-dimensional geometric figures. Examples: Sphere, Cylinders, Cubes, Cones, Pyramids, and Prisms.

Three-Dimensional Figures

Lesson 9-2: Prisms & Pyramids

11.4 Vocabulary Polyhedron Prism, Pyramid, Cylinder, Cone, Sphere

Section 8.2 Pyramids, Area, & Volume

9.1 Prisms, Area, & Volume 8/7/2019 Section 9.1 Nack/Jones.

Presentation transcript:

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. A face is the flat polygonal surfaces of the polyhedron face In a solid prism there will be a maximum of 2 identical faces called bases. base

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

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

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 Triangular Pyramid: Square Pyramid: Pentagonal Pyramid:

A C D F B E G AB is the altitude of the pyramid and will be perpendicular to the base A is the vertex of the pyramid 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. Example 2 Find: a. JKb. PS c. PR J P O M K R S Given: the regular square pyramid shown with altitude PR and slant height PS, perimeter of JKMO = 40, PK = 13 J

Summary Summarize in your own words the vocabulary that you learned today. Homework: Worksheet 9.8