1. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 9.2 Polygons

2. Copyright 2013, 2010, 2007, Pearson, Education, Inc. What You Will Learn Polygons Similar Figures Congruent Figures 9.2-2

3. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Polygons A polygon is a closed figure in a plane determined by three or more straight line segments. 9.2-3

4. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Polygons The straight line segments that form the polygon are called its sides, and a point where two sides meet is called a vertex (plural, vertices). The union of the sides of a polygon and its interior is called a polygonal region. A regular polygon is one whose sides are all the same length and whose interior angles all have the same measure. 9.2-4

5. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Polygons Polygons are named according to their number of sides. Icosagon20Heptagon7 Dodecagon12Hexagon6 Decagon10Pentagon5 Nonagon9Quadrilateral4 Octagon8Triangle3 NameNumber of Sides NameNumber of Sides 9.2-5

6. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Polygons The sum of the measures of the interior angles of an n-sided polygon is (n – 2)180º. SidesTrianglesSum of the Measures of the Interior Angles 311(180º) = 180º 422(180º) = 360º 533(180º) = 540º 644(180º) = 720º 9.2-6

7. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Types of Triangles Acute Triangle All angles are acute. Obtuse Triangle One angle is obtuse. 9.2-7

8. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Types of Triangles (continued) Right Triangle One angle is a right angle. Isosceles Triangle Two equal sides. Two equal angles. 9.2-8

9. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Types of Triangles (continued) Equilateral Triangle Three equal sides. Three equal angles, 60º each. Scalene Triangle No two sides are equal in length. 9.2-9

10. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Similar Figures Two figures are similar if their corresponding angles have the same measure and the lengths of their corresponding sides are in proportion. 4 3 4 6 66 9 4.5 9.2-10

11. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 3: Using Similar Triangles to Find the Height of a Tree Monique Currie plans to remove a tree from her backyard. She needs to know the height of the tree. Monique is 6 ft tall and determines that when her shadow is 9 ft long, the shadow of the tree is 45 ft long (see Figure). How tall is the tree? 9.2-11

12. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 3: Using Similar Triangles to Find the Height of a Tree 9.2-12

13. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 3: Using Similar Triangles to Find the Height of a Tree Solution Let x represent the height of the tree The tree is 30 ft tall. 9.2-13

14. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Congruent Figures If corresponding sides of two similar figures are the same length, the figures are congruent. Corresponding angles of congruent figures have the same measure. 9.2-14

15. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Quadrilaterals Quadrilaterals are four-sided polygons, the sum of whose interior angles is 360º. Quadrilaterals may be classified according to their characteristics. 9.2-15

16. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Quadrilaterals Trapezoid Two sides are parallel. Parallelogram Both pairs of opposite sides are parallel. Both pairs of opposite sides are equal in length. 9.2-16

17. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Quadrilaterals Rhombus Both pairs of opposite sides are parallel. The four sides are equal in length. Rectangle Both pairs of opposite sides are parallel. Both pairs of opposite sides are equal in length. The angles are right angles. 9.2-17

18. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Quadrilaterals Square Both pairs of opposite sides are parallel. The four sides are equal in length. The angles are right angles. 9.2-18

19. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 5: Angles of a Trapezoid Trapezoid ABCD is shown. a) Determine the measure of the interior angle, x. b) Determine the measure of the exterior angle, y. 9.2-19

20. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 5: Angles of a Trapezoid Solution a) Determine the measure of the interior angle, x. 9.2-20

21. Copyright 2013, 2010, 2007, Pearson, Education, Inc. Example 5: Angles of a Trapezoid Solution b) Determine the measure of the exterior angle, y. 9.2-21