Chapter Introductory Geometry 11 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

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Presentation transcript:

Chapter Introductory Geometry 11 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

11-2 Linear Measure  The English System  Converting Units of Measure  Dimensional Analysis (Unit Analysis)  The Metric System  Distance Properties  Distance Around a Plane Figure  Circumference of a Circle  Arc Length Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

The English System Unit Equivalent in Other Units yard3 feet foot12 inches mile1760 yd or 5280 ft Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Converting Units of Measure Convert 5.25 miles to yards 1 mi = 5280 ft, 1 ft = Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Dimensional Analysis (Unit Analysis) Dimensional Analysis a process to convert from one unit of measurement to another. The process works with unit ratios. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Example 11-3 If a cheetah is clocked at 60 miles per hour, what is its speed in feet per second? Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

PrefixSymbolFactor kilok1000 hectoh100 dekada10 decid0.1 centic0.01 millim0.001 The Metric System Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

The Metric System UnitSymbol Relationship to Base Unit kilometerkm1000 m hectometerhm100 m dekameterdam10 m metermbase unit decimeterdm0.1 m centimetercm0.01 m millimetermm0.001 m Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Benchmarks for Metric Units Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Converting Metric Units Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Convert each of the following: a.1.4 km = _________ m b.285 mm = _________ m c.0.03 km = ________cm Example 11-5 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Distance Properties 1.The distance between any two points A and B is greater than or equal to 0 (AB  0). 2.The distance between any two points A and B is the same as the distance between B and A (AB = BA). 3.For any three points, A, B, and C, the distance between A and B plus the distance between B and C is greater than or equal to the distance between A and C (AB + BC  AC). Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Triangle Inequality The sum of the lengths of any two sides of a triangle is greater than the length of the third side. AB + BC > AC Can a triangle be made with sides that are 15 cm, 18 cm, and 37 cm? no Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Distance Around a Plane Figure Perimeter the length of a simple closed curve, or the sum of the lengths of the sides of a polygon. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Example 11-6 Find the perimeter of each of the shapes. 9 cm2ℓ + 2w Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Example 11-6 (continued) 4s4s170 mm What is the perimeter of a regular n-gon with side s? ns Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Circumference of a Circle Circle – the set of all points in a plane that are the same distance from a given point, the center. Circumference – the perimeter of a circle. Pi – the ratio between the circumference of a circle and the length of its diameter. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Arc Length Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

a.The circumference of a circle with radius 2 m b.The radius of a circle with circumference 15π m c.The length of a 25° arc of a circle with diameter 10 cm. d.The radius of an arc whose central angle is 87° and whose arc length is 154 cm. 4π m 7.5 m ≈ cm Example 11-7 Find each of the following: Copyright © 2013, 2010, and 2007, Pearson Education, Inc.