Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Geometry 8 8.1 Basic Geometric Figures 8.2 Perimeter 8.3 Area 8.4 Circles 8.5 Volume and Surface Area 8.6 Relationships Between Angle Measures 8.7 Congruent Triangles and Properties of Parallelograms 8.8 Similar Triangles Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 2

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures a Draw and name segments, rays, and lines. Also, identify endpoints, if they exist. b Name an angle in five different ways, and given an angle, measure it with a protractor. c Classify an angle as right, straight, acute, or obtuse. d Identify perpendicular lines. d Use < or > for  to write a true statement in a situation like 6  10. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 3

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures e Classify a triangle as equilateral, isosceles, or scalene and as right, obtuse, or acute. Given a polygon of twelve, ten, or fewer sides, classify it as a dodecagon, a decagon, and so on. f Given a polygon of n sides, find the sum of its angle measures using the formula (n – 2) 80 . d Use < or > for  to write a true statement in a situation like 6  10. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 4

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures a Draw and name segments, rays, and lines. Also, identify endpoints, if they exist. A segment is a geometric figure consisting of two points, called endpoints, and all points between them. The segment whose endpoints are A and B is shown below. It can be named Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 5

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures a Draw and name segments, rays, and lines. Also, identify endpoints, if they exist. A ray consists of a segment, say and all points X such that B is between A and X, that is, and all points “beyond” B. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 6

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures a Draw and name segments, rays, and lines. Also, identify endpoints, if they exist. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 7

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures a Draw and name segments, rays, and lines. Also, identify endpoints, if they exist. Lines in the same plane are called coplanar. Coplanar lines that do not intersect are called parallel. For example, lines l and m below are parallel Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 8

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures a Draw and name segments, rays, and lines. Also, identify endpoints, if they exist. The figure below shows two lines that cross. Their intersection is D. They are also called intersecting lines. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 9

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures b Name an angle in five different ways, and given an angle, measure it with a protractor. An angle is a set of points consisting of two rays, or half-lines, with a common endpoint. The endpoint is called the vertex of the angle. The rays are called the sides of the angle. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 10

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures b Name an angle in five different ways, and given an angle, measure it with a protractor. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 11

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures b Name an angle in five different ways, and given an angle, measure it with a protractor. Measuring angles is similar to measuring segments. The unit most commonly used for angle measure is the degree. Below is such a unit. Its measure is 1 degree, or 1°. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 12

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures b Name an angle in five different ways, and given an angle, measure it with a protractor. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 13

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures b Name an angle in five different ways, and given an angle, measure it with a protractor. A device called a protractor is used to measure angles. Protractors have two scales. To measure an angle like below, we place the protractor’s at the vertex and line up one of the angle’s sides at Then we check where the angle’s other side crosses the scale. In the figure, is on the inside scale, so we check where the angle’s other side crosses the inside scale. We see that m ∠Q = 145°. The notation m ∠Q is read “the measure of angle Q.” Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 14

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures b Name an angle in five different ways, and given an angle, measure it with a protractor. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 15

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures b Name an angle in five different ways, and given an angle, measure it with a protractor. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 16

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures TYPES OF ANGLES Right angle: An angle whose measure is 90 . Straight angle: An angle whose measure is 180 . Acute angle: An angle whose measure is greater than and less than 90 . Obtuse angle: An angle whose measure is greater than and less than 180°. c Classify an angle as right, straight, acute, or obtuse. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 17

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures c Classify an angle as right, straight, acute, or obtuse. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 18

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures c Classify an angle as right, straight, acute, or obtuse. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 19

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures d Identify perpendicular lines. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 20

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures e Classify a triangle as equilateral, isosceles, or scalene and as right, obtuse, or acute. Given a polygon of twelve, ten, or fewer sides, classify it as a dodecagon, a decagon, and so on. The figures below are examples of polygons. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 21

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures e Classify a triangle as equilateral, isosceles, or scalene and as right, obtuse, or acute. Given a polygon of twelve, ten, or fewer sides, classify it as a dodecagon, a decagon, and so on. A triangle is a polygon made up of three segments, or sides. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 22

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures TYPES OF TRIANGLES Equilateral triangle: All sides are the same length. Isosceles triangle: Two or more sides are the same length. Scalene triangle: All sides are of different lengths. Right triangle: One angle is a right angle. Obtuse triangle: One angle is an obtuse angle. Acute triangle: All three angles are acute. e Classify a triangle as equilateral, isosceles, or scalene and as right, obtuse, or acute. Given a polygon of twelve, ten, or fewer sides, classify it as a dodecagon, a decagon, and so on. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 23

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures e Classify a triangle as equilateral, isosceles, or scalene and as right, obtuse, or acute. Given a polygon of twelve, ten, or fewer sides, classify it as a dodecagon, a decagon, and so on. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 24

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures SUM OF THE ANGLE MEASURES OF A TRIANGLE f Given a polygon of n sides, find the sum of its angle measures using the formula (n – 2) 80 . Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 25

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures f Given a polygon of n sides, find the sum of its angle measures using the formula (n – 2) 80 . 1 Find the missing angle measure. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 26

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures f Given a polygon of n sides, find the sum of its angle measures using the formula (n – 2) 80 . 1 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 27

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures SUM OF ANGLE MEASURES f Given a polygon of n sides, find the sum of its angle measures using the formula (n – 2) 80 . Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 28

Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 8.1 Basic Geometric Figures f Given a polygon of n sides, find the sum of its angle measures using the formula (n – 2) 80 . 2 What is the sum of the angle measures of a hexagon? Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 29