1. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 6 Geometry

2. Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 6.2 Plane Figures and Solids

3. Martin-Gay, Developmental Mathematics, 2e 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Identifying Plane Figures A plane figure is a figure that lies on a plane. A plane figure, like planes, have length and width but no thickness or depth.

4. Martin-Gay, Developmental Mathematics, 2e 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Polygons DefinitionExample Polygon - A closed plane figure that basically consists of three or more line segments that meet their end points. Regular polygon - A closed plane figure whose sides are all the same length and whose angles are the same measure. A B C D E F G H I J E

5. Martin-Gay, Developmental Mathematics, 2e 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Polygons Number of SidesExampleFigure Examples 3TriangleA, F 4QuadrilateralB,E,G 5PentagonH 6HexagonI 7HeptagonC 8OctagonJ 9NonagonK 10DecagonD Refer to the figures on the previous slide.

6. Martin-Gay, Developmental Mathematics, 2e 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the measure of Since the sum of the measures of the three angles is 180 ̊, we have measure of

7. Martin-Gay, Developmental Mathematics, 2e 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Triangles Triangle Classification EquilateralIsoscelesScalene All three sides are the same length. Also, all three angles have the same measure. Two sides are the same length. Also, the angles opposite the equal sides have equal measure. No sides are the same length. No angles have the same measure.

8. Martin-Gay, Developmental Mathematics, 2e 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the measure of We know that the measure of the right angle is 90 . Since the sum of the measures of the angles is 180 , we have

9. Martin-Gay, Developmental Mathematics, 2e 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Special Quadrilaterals Parallelogram – opposite sides are parallel and equal in length. Rectangle – special parallelogram that has four right angles. Square – special rectangle that has all four sides equal in length. Rhombus – special parallelogram that has all four sides equal in length. Trapezoid – quadrilateral with exactly one pair of opposite sides parallel.

10. Martin-Gay, Developmental Mathematics, 2e 10 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Circles DefinitionExample Circle - A plane figure that consists of all points that are the same fixed distance from a point c, called the center. Radius - The distance from the center of the circle to any point on the circle. Diameter - The distance across the circle passing through the center. center radius diameter

11. Martin-Gay, Developmental Mathematics, 2e 11 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Identifying Solid Figures DefinitionExample Solid - A figure that lies in space and has length, width, and height or depth. Rectangular solid - A solid that consists of six sides, or faces, all of which are rectangles. Cube - A rectangular solid whose six sides are squares. Pyramid - The pyramids we will study have square bases and heights that are perpendicular to their base. Width Height Length Height Square base

12. Martin-Gay, Developmental Mathematics, 2e 12 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Spheres DefinitionExample Sphere - Consists of all points in space that are the same distance from a point c, called the center of the sphere Radius - The distance from the center to the sphere. Diameter - The distance across the sphere passing through the center. Radius Diameter Center

13. Martin-Gay, Developmental Mathematics, 2e 13 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the radius of the sphere. The radius is half the diameter. The radius is 18 feet.

14. Martin-Gay, Developmental Mathematics, 2e 14 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Cylinders and Cones DefinitionExample Cylinders - The cylinders we will study are in the shape of circles and have heights that are perpendicular to their base. Cones - The cones we will study have bases that are circles and heights that are perpendicular to their base. Height Circular base