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

Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Section 9.2

Polygons


What You Will Learn

PolygonsSimilar FiguresCongruent Figures

9.2-2


Polygons

A polygon is a closed figure in a plane determined by three or more straight line segments.

9.2-3


PolygonsThe 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


PolygonsPolygons are named according to their number of sides.

Icosagon20Heptagon7

Dodecagon12Hexagon6

Decagon10Pentagon5

Nonagon9Quadrilateral4

Octagon8Triangle3

NameNumber of Sides

NameNumber of Sides

9.2-5


Polygons

The sum of the measures of the interior angles of an n-sided polygon is (n – 2)180º.

Sides Triangles

Sum of the Measures of the Interior Angles

3 1 1(180º) = 180º

4 2 2(180º) = 360º

5 3 3(180º) = 540º

6 4 4(180º) = 720º

9.2-6


Types of Triangles

Acute TriangleAll angles are acute.

Obtuse TriangleOne angle is obtuse.

9.2-7


Types of Triangles (continued)

Right TriangleOne angle is a right angle.

Isosceles Triangle

Two equal sides.Two equal angles.

9.2-8


Types of Triangles (continued)

Equilateral TriangleThree equal sides. Three equal angles, 60º each.

Scalene TriangleNo two sides are equal in length.

9.2-9


Similar FiguresTwo 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

6 6

9

4.5

9.2-10


Example 3: Using Similar Triangles to Find the Height of a TreeMonique 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


Example 3: Using Similar Triangles to Find the Height of a Tree

9.2-12


Example 3: Using Similar Triangles to Find the Height of a TreeSolutionLet x represent the height of the tree

height of tree

height of Monique

length of tree's shadow

length of Monique's shadow

x

6

45

9

9x 270 x 30

The tree is 30 ft tall.9.2-13


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


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


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


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


Quadrilaterals

Square

Both pairs of opposite sides are parallel. The four sides are equal in length. The angles are right angles.

9.2-18


Example 5: Angles of a TrapezoidTrapezoid ABCD is shown.a) Determine the measure of the interior angle, x.b) Determine the measure of the exterior angle, y.

9.2-19


Example 5: Angles of a TrapezoidSolutiona) Determine themeasure of theinterior angle, x.

mRDAB mRABC mRABC mRx 360

130 90 90 mRx 360

310 mRx 360 mRx 50

9.2-20


Example 5: Angles of a TrapezoidSolutionb) Determine themeasure of theexterior angle, y.

mRx mRy 180

mRy 180 mRx

mRy 180 50

mRy 1309.2-21

Date post:	11-Jan-2016
Category:	Documents
Upload:	rebecca-mathews
View:	215 times
Download:	2 times

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

Documents