math 1 march 13 th warm-up: 1.which point of concurrency would be equidistant from each road on the...

Math 1 March 13th

WARM-UP:1. Which point of concurrency would be equidistant from each road on the map?

2. TQ = 5 TS = 12 RU = 6 Find the measures of

these segments:a) TRb) SUc) SV

Main

Stre

et

1st Avenue

Highway 31

Correct Quizzes• Altitudes• Orthocenter• Medians• Centroid• Perpendicular bisectors• Circumcenter• Angle bisectors• Incenter• Incenter• Circumcenter

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?

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

Nonagon

Decagon

Dodecagon

n-gon

F

A B

C

DE

Important TermsA 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.

More Important Terms

EQUILATERAL - All sides are congruentEQUIANGULAR - All angles are congruentREGULAR - All sides and angles are congruent

Polygons are named by listing its vertices consecutively.

A B

E D

CF

Polygons can be CONCAVE or CONVEX

CONVEX

CONCAVE

Ex. 3 Classify each polygon as convex or concave.

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°

# of sides

# of triangles

Sum of measures of

interior angles

3 1 1(180) = 180

4 2 2(180) = 360

5 3 3(180) = 540

6 4 4(180) = 720

n n-2 (n-2) 180

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

interior angles is (n – 2)(180°)

Ex. 1 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

If 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

If 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

If any convex polygon, the sum of the measures of the

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

1

3

2

4

m m m m 1 2 3 4 360

Ex. 2 Find the measure of ONE exterior angle of a regular hexagon.

60°

sum of the exterior anglesnumber of sides

3606

Ex. 3 Find the measure of ONE exterior angle of a regular heptagon.

51.4°

sum of the exterior anglesnumber of sides

3607

Ex. 4 Each exterior angle of a polygon is 18. How many sides does it have?

n = 20

angleexterior sides ofnumber

anglesexterior theof sum

18360

n

Ex. 5 The sum of the measures of five interior angles of a hexagon is 535. What is the measure of the sixth angle?

185°

Ex. 6 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°

Ex. 7 If each interior angle of a regular polygon is 150, then how many sides does the polygon have?

n = 12