…with a little review

Ch 9-8Interior & Exterior Angles of Polygons?

C. N. ColonGeometry

REVIEW: Ch 9-6 and Ch 9-7

Proving Triangles Congruent by

(AAS, HL)

PostulatesAAS If two angles and a non included side of one triangle are

congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent.

HL If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and corresponding leg of another right triangle, then the triangles are congruent.

A

B C

D

E F

A

B C

D

E F

Problem

Statements Reasons

Step 1: Mark the Given Step 2: Mark vertical angles

Step 3: Choose a Method (SSS /SAS/ASA/AAS/ HL )Step 4: List the Parts in the order of the method

Step 5: Fill in the reasonsStep 6: Is there more?

AAS

Given

Given

Vertical Angle Thm

AAS Postulate

Given: A C BE BDProve: ABE CBD

E

C

D

AB

1. A C2. ABE CBD

3. BE BD4. ABE CBD

3. AC AC

2. AB AD

1. ,ABC ADCright s

Statements Reasons

Step 1: Mark the Given Step 2: Mark reflexive sidesStep 3: Choose a Method (SSS /SAS/ASA/AAS/ HL )Step 4: List the Parts in the order of the methodStep 5: Fill in the reasonsStep 6: Is there more?

HL

Given

Given

Reflexive Property

HL Postulate

Given: ABC, ADC right s AB ADProve: ABC ADC

CB D

A

4. ABC ADC

C. N. Colόn

Geometry

Ch 9-8 Interior and Exterior Angles of Polygons

POLYGONS

What does the word “polygon” mean?

What is the smallest number of sides a polygon can have?

What is the largest number of sides a polygon can have?

POLYGONS

EQ: How do I find the measure of an interior & exterior angle of a polygon?

10/17/2007

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

Nonagon

Decagon

Dodecagon

n-gon

Important Terms

F

A B

C

DE

A VERTEX is the point of intersection of two sides

A segment whose endpoints

are two nonconsecutive vertices is called a DIAGONAL.

CONSECUTIVE VERTICES are two endpoints of any side.

Sides that share a vertex are called CONSECUTIVE SIDES.

POLYGONS

More Important Terms

EQUILATERAL - All sides are congruent

EQUIANGULAR - All angles are congruent

REGULAR - All sides and angles are congruent

POLYGONS

10/17/2007

What is the sum of the measures of the interior angles of a triangle?

180°180°

What is the sum of the measures of the interior angles of any

quadrilateral?

REVIEW:

180°

360°

If a convex polygon has n sides, then the sum of the measure of the

interior angles is (n-2)(180°)

By the way concave is the opposite of convex. A concave polygon has sides that “collapse” inward

Use the regular pentagon to answer the questions.

A) Find the sum of the measures of the interior angles.

B) Find the measure of ONE interior angle

540°

108°

Two more important terms

Exterior Angles

Interior Angles

In any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is

360°.

1

2

3

4

5

m m m m m 1 2 3 4 5 360

In any convex polygon, the sum of the measures

of the exterior angles, one at each vertex, is 360°.

1

3

2

m m m 1 2 3 360

Find the measure of ONE exterior angle of a regular hexagon.

60°

sum of the exterior anglesnumber of sides

3606

Find the measure of ONE exterior angle of a regular heptagon.

51.4°

sum of the exterior anglesnumber of sides

3607

The sum of the measures of five interior angles of a hexagon is 535. What is the measure of the sixth angle?

185°

The measure of the exterior angle of a quadrilateral are x, 3x, 5x, and 3x. Find the measure of each angle.

30°, 90°, 150°, and 90°

The sum of the interior angles of a polygon is 720. Find the number of sides.

n = 6

HW: p. 371 #4-20 (mo4)

… tomorrow’s HW is the Ch. 9 Reviewp. 375 # 1-25 (all)