Modeling with Geometry Copyright © 2011 Pearson Education, Inc.

Fundamentals of Geometry Unit 10A Fundamentals of Geometry Copyright © 2011 Pearson Education, Inc.

Points, Lines, and Planes A geometric point is imagined to have zero size. A geometric line is formed by connecting two points along the shortest possible path. Line segments are pieces of a line. A geometric plane is a perfectly flat surface that has infinite length and width, but no thickness. Copyright © 2011 Pearson Education, Inc.

Dimension The dimension of an object can be thought of as the number of independent directions in which you could move if you were on the object. We can also think about dimension by the number of coordinates required to locate a point. Copyright © 2011 Pearson Education, Inc.

Angles The intersection of two lines or line segments forms an angle. The point of intersection is called the vertex. Copyright © 2011 Pearson Education, Inc.

Types of Angles Right: measures 90 Straight: measures 180 Acute: measures less than 90 Obtuse: measures between 90 and 180 Copyright © 2011 Pearson Education, Inc.

CN 1a-d Angles Find the degree measure of the angles that subtrahend A. a semicircle B. a quarter circle C. an eighth of a circle D. a hundredth of a circle Copyright © 2011 Pearson Education, Inc.

Plane Geometry Plane geometry is the geometry of two-dimensional objects. Circles All points on a circle are located at the same distance—the radius—from the circle’s center. The diameter of a circle is twice its radius. Copyright © 2011 Pearson Education, Inc.

Plane Geometry A polygon is any closed shape in the plane made from straight line segments. A regular polygon is a polygon in which all the sides have the same length and all interior angles are equal. Copyright © 2011 Pearson Education, Inc.

Perimeter and Area Copyright © 2011 Pearson Education, Inc.

CN 2 Interior Design A window consists of a 4 foot by 6 foot rectangle capped by a semicircle. How much trim is needed to go around the window? Copyright © 2011 Pearson Education, Inc.

CN 3 Building Stairs You have built a stairway in a new house and want to cover the space beneath the stairs with plywood. What is the area of this region? Copyright © 2011 Pearson Education, Inc.

CN 4 City Park A one block city park is bound by two sets of parallel streets. The streets along the block are each 55 yards long and the perpendicular distance between the streets is 39 yards. How much sod should be purchased to cover ther entire park in grass? Copyright © 2011 Pearson Education, Inc.

Three-Dimensional Geometry Copyright © 2011 Pearson Education, Inc.

Three-Dimensional Geometry Example: A water reservoir has a rectangular base that measures 30 meters by 40 meters, and vertical walls 15 meters high. It was filled to capacity, and after a month the water depth was 6 meters. How much water was used? Volume of water at the beginning: Volume of water after a month: The amount used was 18,000 m3 – 7200 m3 = 10,800 m3. Copyright © 2011 Pearson Education, Inc.

CN 5 Water Reservoir A water reservoir has a rectangular base that measures 30 meters by 40 meters, and vertical walls 15 meters high. At the beginning of the summer, the reservoir was filled to capacity. At the end of the summer, the water depth was 4 meters. How much water was used? Copyright © 2011 Pearson Education, Inc.

CN 6 Comparing Volumes Which holds more soup, a can with a diameter of 3 inches and a height of 4 inches or a can with a diameter of 4 inches and a height of 3 inches? Copyright © 2011 Pearson Education, Inc.

The Five Perfect Solids Plato formed ideas about geometry and the universe involving the five perfect solids, shown below. Each of the perfect solids is such that all of its faces are the same regular polygon. Copyright © 2011 Pearson Education, Inc.

Scaling Laws Lengths scale with the scale factor. Areas scale with the square of the scale factor. Volumes scale with the cube of the scale factor. Copyright © 2011 Pearson Education, Inc.

CN 7a-c Doubling your Size Suppose that, magically, your size suddenly doubled—that is your height, width, and depth doubled. For example, if you were 5 feet tall before, you now are 10 feet tall. A. By what factor has your waist size increased? B. How much more material will be required for your clothes? C. By what factor has your weight changed? Copyright © 2011 Pearson Education, Inc.

The Surface-Area-to-Volume Ratio The surface-area-to-volume ratio for any object is its surface area divided by its volume: Larger objects have smaller surface-area-to- volume ratios than similarly proportioned small objects. Smaller objects have larger surface-area-to-volume ratios than similarly proportioned small objects. Copyright © 2011 Pearson Education, Inc.

CN 8 Chilled Drink Suppose you have a few ice cubes and you want to cool your drink quickly. Should you crush the ice before you put it into your drink? Why or why not? Copyright © 2011 Pearson Education, Inc.

Homework 10A Fundamentals of Geometry Class Notes 1-8 Quick Quiz p.563: 1-10 Exercises p.563: 1-16 1 web 1world Copyright © 2011 Pearson Education, Inc.

Web and World 88. The Geometry of Ancient Cultures 89. Surveying and GIS 90. Platonic Solids ------------------------- 91.Geometry in the News 92. Geometric Idealizations 93. Circles and Polygons 94. Three-Dimensional Objects Copyright © 2011 Pearson Education, Inc.