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Classification of curves Simple, not closed Simple, closed Closed, - - PowerPoint PPT Presentation

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Classification of curves Simple, not closed Simple, closed Closed, not simple Not simple, not closed MA202 Sections 5 & 401 Chapter 11-2 Slides Interior and exterior of a simple closed curve MA202 Sections 5 & 401 Chapter 11-2

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Classification of curves

Simple, not closed Simple, closed Closed, not simple Not simple, not closed

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Interior and exterior of a simple closed curve

MA202 Sections 5 & 401 Chapter 11-2 Slides

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SLIDE 3

Jordan Curve Theorem

MA202 Sections 5 & 401 Chapter 11-2 Slides

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SLIDE 4

Example 11.7

Is the red dot interior or exterior to each curve?

MA202 Sections 5 & 401 Chapter 11-2 Slides

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SLIDE 5

Example 11.7 - Determining Interior Points

Is the red dot interior or exterior to each curve?

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Jordan Curve Theorem

MA202 Sections 5 & 401 Chapter 11-2 Slides

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SLIDE 7

Example 11.8 - Counting Regions in the Plane

MA202 Sections 5 & 401 Chapter 11-2 Slides

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SLIDE 8

Example 11.8 - Counting Regions in the Plane

MA202 Sections 5 & 401 Chapter 11-2 Slides

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SLIDE 9

Convex Regions

MA202 Sections 5 & 401 Chapter 11-2 Slides

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SLIDE 10

Concave Regions

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Classification of Polygonal Curves

Simple polygonal curve Nonsimple polygonal curve Nonsimple closed polygonal curve

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Classification of Polygonal Curves

Nonconvex polygon Convex polygon Polygonal region

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Names of Polygons

Triangle Quadrilateral Pentagon

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Names of Polygons

Hexagon Heptagon Octagon

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Names of Polygons

Nonagon Decagon 12-gon

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Angles in a convex polygon

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Sum of Angle Measures in a Convex Polygon

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Example 11.9 - Finding the Angles in a Pentagonal Arch

Find the measures of 3x, 8x, y and z.

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Sum of Interior Angle Measures of a General Polygon

MA202 Sections 5 & 401 Chapter 11-2 Slides

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SLIDE 20

Example 11.10 - Measuring the Angles in a Star

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Total Turns Theorem

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Example 11.11 - Finding Total Turns

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Example 11.11 - Finding Total Turns

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Classifying Triangles

Acute Right Obtuse

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Classifying Triangles

Scalene Isosceles Equilateral

MA202 Sections 5 & 401 Chapter 11-2 Slides

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SLIDE 26

Example 11.12 - Classifying Triangles

Classify each triangle: △ABC, △ACD, △ACE, △AED, △AFE and △CDE

MA202 Sections 5 & 401 Chapter 11-2 Slides

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SLIDE 27

Example 11.12 - Classifying Triangles

MA202 Sections 5 & 401 Chapter 11-2 Slides

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SLIDE 28

Example 11.12 - Classifying Triangles

O & I R & S A & E R & S O & I O & I

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Classifying Quadrilaterals

Kite Trapezoid Isosceles trapezoid

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Classifying Quadrilaterals

Parrallelogram Rhombus Rectangle Square

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Classifying Quadrilaterals

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Equilateral, Equiangular and Regular

Equilateral Equiangular Regular

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Interior, Exterior and Central Angles

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Circles

MA202 Sections 5 & 401 Chapter 11-2 Slides

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Discussion Questions

Can a line cross a simple closed curve 99 times? Draw the figures that satisfy the given description:

A nonsimple closed four-sided polygonal curve A concave pentagon An equiangular quadrilateral A convex octagon

Decide if each of the following statements are true or false:

Rectangles are always squares. Squares are always rectangles. Rhombuses are never squares. Trapezoids are sometimes squares.

MA202 Sections 5 & 401 Chapter 11-2 Slides

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SLIDE 36

Homework

Homework 5 (due 3/9/10): Section 11.1 #1, 4, 11, 15, 17, 21, 45 Section 11.2 #1, 4, 6, 7, 16, 17, 18, 20, 22

MA202 Sections 5 & 401 Chapter 11-2 Slides