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Chapter 3

Chapter 3. Geometry and Measurement. What You Will Learn:. To identify, describe, and draw: Parallel line segments Perpendicular line segments To draw: Perpendicular bisectors Angle bisectors Generalize rules for finding the area of: Parallelograms Triangles

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Chapter 3

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  1. Chapter 3 Geometry and Measurement

  2. What You Will Learn: • To identify, describe, and draw: • Parallel line segments • Perpendicular line segments • To draw: • Perpendicular bisectors • Angle bisectors • Generalize rules for finding the area of: • Parallelograms • Triangles • Explain how the area of a rectangle can be used to find the area of: • Parallelograms • Triangles

  3. 3.1 – Parallel and Perpendicular Line Segments • What you will learn: • To identify, describe, and draw: • Parallel line segments • Perpendicular line segments

  4. Parallel • Describes lines in the same plane that never cross, or intersect • The perpendicular distance btw parallel line segments must be the same at each end of the line segments. • They are always marked using “arrows” • http://www.mathopenref.com/parallel.html

  5. Some ways to create parallel line segments: • Using paper folding • Using a ruler and a right triangle Example: • Draw a line segment, AB. Draw another line segment, CD, parallel to AB.

  6. Example: • Draw a line segment, AB. Draw another line segment, CD, parallel to AB. D B B Use a ruler to draw a line segment. A A C Slide the triangle, draw a parallel line. D B A C Label the endpoints (A, B, C, D). Mark the lines with arrows to show the lines are parallel.

  7. Perpendicular • Describes lines that intersect at right angles (90°) • They are marked using a small square • http://www.mathopenref.com/perpendicular.html right angle

  8. Some ways to create perpendicular line segments: • Using paper folding (p. 85) • Using a ruler and protractor (p. 85) • http://www.mathopenref.com/constperplinepoint.html

  9. Assignment • P. 86 • #1, 3-5, 7, 9, 11, Math Link • Still Good? #2, 8, 10, 12, 13 • ProStar? #14-16 right angle

  10. 3.2 – Draw Perpendicular Bisectors • Bisect: • Bi means “two.” Sect means “cut.” So, Bisect means to cut in two. • Perpendicular bisector • A line that divides a line segment in half and is at right angles (90°) to the line segment. • Equal line segments are marked with “hash” marks

  11. Some ways to create a perpendicular bisector: • Using a compass (p. 90) • http://www.mathopenref.com/constbisectline.html • Using a ruler and a right triangle (p. 91) • Using paper folding (p. 91)

  12. Assignment • P. 92, # 1-5, 8 • Still Good? # 6, 7, 9, MathLink • ProStar? #10

  13. 3.3 – Draw Angle Bisectors • Terms: • Acute angle • An angle that is less than 90° • Obtuse angle • An angle that is more than 90° • Angle Bisector • A line that divides an angle into two equal parts • Equal angles are marked with the same symbol Less than 90° Greater than 90°

  14. Some ways to create an angle bisector include: • Using a ruler and compass (p. 95) • http://www.mathopenref.com/constbisectangle.html • Using a ruler and protractor (p. 95) • Using paper folding (p.95)

  15. Assignment • P. 97, # 1 & 2, 5, 6, 8 • Still Good? # 3 & 4, 9, 11, 13, MathLink • ProStar? #12, 14, 15 Less than 90°: acute Greater than 90°: obtuse Angle Bisector

  16. 3.4 – Area of a Parallelogram • Area of a rectangle: Area = length x width • Parallelogram • A four-sided figure with opposite sides parallel and equal in length • http://www.mathopenref.com/parallelogramarea.html 6 cm A = l x w A = 6 cm x 4 cm A = 24 cm w 4 cm 2 l

  17. Making a Parallelogram from a Rectangle cut paste

  18. Base • A side of a two-dimensional closed figure • Common symbol is b • Height • The perpendicular distance from the base to the opposite side • Common symbol ish • Suggest a formula for calculating the area of a parallelogram. h b

  19. Area of a Rectangle vs. Area of a Parallelogram 8 cm 8 cm 12 cm 12 cm Are they the same? Try it! Area = length x width = 12 cm x 8 cm = 96 cm Area = base x height = 12 cm x 8 cm = 96 cm 2 2 Sometimes it is necessary to extend the line of the base to measure the height h b

  20. Key Ideas • The formula for the area of a rectangle can be used to determine the formula for the area of a parallelogram. • The formula for the area of a parallelogram is A = b x h, where b is the base and h is the height. • The height of a parallelogram is ALWAYS perpendicular to its base. h b

  21. Assignment • P. 104, # 1-3, 5, 7, 9, 11 • Still Good? # 13-18, MathLink • ProStar? # 19, 20 h A = b x h b

  22. 3.5 – Area of a Triangle • What you will learn: • Develop the formula for the area of a triangle • Calculate the area of a triangle • What we know: • The area of a rectangle • A = l x w • The area of a parallelogram • A = b x h

  23. Key Ideas • The formula for the area of a rectangle or parallelogram can be used to determine the formula for the area of a triangle • The formula for the area of a triangle is A = b x h 2, or A = b x h, 2 where b is the base of the triangle and h is the height of the triangle. • The height of the triangle is always measured perpendicular to its base. • http://www.mathopenref.com/trianglearea.html Cut the rectangle in half h h b b A = b x h 2 A = b x h Cut the area in half

  24. Your Assignment • P. 113, #1-3 as a class. • Area of a Triangle, Notebook • Area of a Triangle Questions, Notebook • P. 113, #4a), 5b) • No problem? #8, 10, 11 • Still good? #13-15 • Pro Star? #16-19

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