Friday, Feb. 22, 2013

Agenda:• TISK & No MM• HW Check• Lesson 10-1: Polygons• Homework: 10-1 problems in packet

TISK Problems1. Simplify:

2. Find the slope of a line through the points (3, -8) and (12, -8).

3. Find sin(A).

A

B C

35

21

HW Check

1) 0.42262) 0.98483) 0.50004) 0.35845) 0.97446) 0.48487) 4.01088) 0.50009) 2.475110) 0.5317

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§10.1 Polygons

Definitions: Polygon

A plane figure that… Is formed by 3 or more segments called sides and… ..each side intersects exactly 2 other sides, one at each

endpoint.

Polygon Not a Polygon

Definitions… Convex

No line that contains a side of the polygon also contains a point in the interior of the polygon.

Concave Not convex (also called

nonconvex) Has a “cave in”

§10.1 Polygons

EquilateralAll sides are

congruentEquiangular

All angles are congruent

RegularBoth equilateral

AND equiangular

§10.1 Polygons

Diagonal A segment that joins two nonconsecutive vertices.

§10.1 Polygons

Names of PolygonsName Number of Sides

Triangle 3

Quadrilateral 4Pentagon 5Hexagon 6

Heptagon 7

Octagon 8

Nonagon 9

Decagon 10

Dodecagon 12n-gon n

§10.1 Polygons

Interior Angles Polygon Interior Angles Theorem

The sum of the measures of the interior angles of a convex polygon is

Corollary to Polygon Interior Angles Theorem The measure of each interior angle of a

regular n-gon is: or

§10.1 Polygons

Exterior Angles Polygon Exterior Angles Theorem

The sum of the measures of the exterior angles of a convex polygon (one angle at each vertex) is 360º.

Corollary to Polygon Exterior Angles Theorem The measure of each exterior angle of a

regular n-gon is or

§10.1 Polygons

Practice If each interior angle of a regular n-gon

is 108º, how many sides does the polygon have?

1 ( 2) 180n n ( 2) 180n

n

108

1 ( 2) 180 nn n108 n

( 2) 180 n108 n

180 360n108 n108 n108 n

0 72 360 n360 72 n5n

108

( 2) 180 n

nn

108 n

( 2) 180 n108 n

§10.1 Polygons

Practice Find the value of x. 89 1x

(45 1)x

(40 41)x

(39 )x

12(64 ) x

12(63 )x

40 340 x180( 2) n180(6 2)

72040 340 x40 340 x

680 340x

2x

§10.1 Polygons