2.5

2.5

How Can See It?Pg. 20

Classify Polygons

2.5 – How Can I See It?______________Classify Polygons

In this section you will discover the names of the many different polygons and how they are classified.

2.28 –EXTERIOR ANGLE OF TRIANGLES a. Compare the interior and exterior angle of the following triangles at right. What do you notice?

70°

55°

ba

c d

a+b+c = 180

Exterior Angle of a Triangle

c+d = 180a+b+c = c+d

a+b = d

ba

c d

Sum of two interior angles equals exterior angle

Exterior Angle of a Triangle

b. Find the measure of the exterior angles.

50 + 70 = x120 = x

5x + 45 = 6x + 3045 = x + 3015 = x

6(15) + 30

120°

Polygon:

2. No sides overlap3. No curved sides

1. Has at least 3 sides

Side: Line segment forming the polygon

M

T

SR

Q

QM

MT

TS

SR

RQ

Vertex: Point where two sides meet

M

T

SR

Q

MTS

R

Q

Consecutive Sides: Two sides that share a point, one after the other

M

T

SR

Q

and MTQM

and QRQM

Diagonal: Segment that joins two nonconsecutive sides M

T

SR

Q

QT

QS

MS

MR

TR

# of sides Name345

trianglequadrilateral

pentagon

# of sides Name3456789

101112n

trianglequadrilateral

pentagonhexagonheptagonoctagon

nonagondecagon

11-gondodecagonn-gon

Convex: No corners point inside the shape

Concave: Not convex! A corner points inside the shape

1. State whether the shape is a polygon. If yes, is it concave or convex? If no, why not?

Curved side

Yes, Concave or ConvexOR

No, _________________

1. State whether the shape is a polygon. If yes, is it concave or convex? If no, why not?

Yes, Concave or ConvexOR

No, _________________

1. State whether the shape is a polygon. If yes, is it concave or convex? If no, why not?

Yes, Concave or ConvexOR

No, _________________

1. State whether the shape is a polygon. If yes, is it concave or convex? If no, why not?

Yes, Concave or ConvexOR

No, ____________________Overlaps

Equilateral Equiangular Regular

All sides are congruent

All angles are congruent

All sides AND all angles are congruent

2. Classify the name of the polygon by the number of sides. Is the polygon equilateral, equiangular, regular, or neither?

Equilateral

Pentagon

a.

b.

Regular

quadrilateral

c.

Equiangular

Octagon

d.

Regular

Heptagon

e.

equilateral

decagon

f.

neither

Hexagon

3. Given the following shapes are regular, solve for x.

10x – 27 = 6x + 174x – 27 = 17

4x = 44x = 11

x2+12x–106 = x2–6x–1618x – 106 = –16

18x = 90x = 5

x2+8 = x2+2x–28 = 2x – 2

10 = 2x5 = x