1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides...

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1.6 – Classify Polygons

description

Side: Line segment forming the polygon M T S R Q

Transcript of 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides...

Page 1: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

1.6 – Classify Polygons

Page 2: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

Polygon:

Plane figure that is formed by 3 or more segments, called sides such that:

1. Each side intersects exactly 2 other sides, once at each endpoint

2. No sides with a common endpoint are collinear

3. No curved sides

Page 3: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

Side: Line segment forming the polygon

M

T

SR

Q

QM

MT

TS

SR

RQ

Page 4: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

Vertex: Point where two sides meet

M

T

SR

Q

MTS

R

Q

Page 5: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

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

M

T

SR

Q

and MTQM

and QRQM

Page 6: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

Diagonal: Segment that joins two nonconsecutive sides

M

T

SR

Q

QT

QS

MS

MR

TR

Page 7: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

# of sides Name3456789

101112n

trianglequadrilateral

pentagonhexagonheptagonoctagon

nonagondecagon

? Extra Credit!dodecagon

n-gon

Page 8: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

Convex: No line that contains a side of the polygon contains a point in the interior of the polygon. (rubberband)

Concave: Not convex! Think of a cave going inward!

Page 9: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

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, _________________

Page 10: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

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

Yes, Concave or ConvexOR

No, _________________

Page 11: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

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

Yes, Concave or ConvexOR

No, _________________

Page 12: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

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

Yes, Concave or ConvexOR

No, ____________________Side touches 3 other sides

Page 13: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

Equilateral Equiangular Regular

All sides are congruent

All angles are congruent

All sides AND all angles are congruent

Page 14: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

Classify the name of the polygon by the number of sides. Is the polygon equilateral, equiangular, or regular? Explain your reasoning.

Regular

Hexagon

All sides and angles

Page 15: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

Classify the name of the polygon by the number of sides. Is the polygon equilateral, equiangular, or regular? Explain your reasoning.

Regular

quadrilateral

All sides and angles

Page 16: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

Classify the name of the polygon by the number of sides. Is the polygon equilateral, equiangular, or regular? Explain your reasoning.

Equiangular

Octagon

All angles , but not all sides

Page 17: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

Classify the name of the polygon by the number of sides. Is the polygon equilateral, equiangular, or regular? Explain your reasoning.

equilateral

decagon

All sides , but not all angles

Page 18: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

Classify the name of the polygon by the number of sides. Is the polygon equilateral, equiangular, or regular? Explain your reasoning.

Regular

Heptagon

All sides and angles

Page 19: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

Classify the name of the polygon by the number of sides. Is the polygon equilateral, equiangular, or regular? Explain your reasoning.

Equilateral

Quadrilateral

All sides , but not all angles

Page 20: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

3. The lengths (in feet) of two sides of a regular quadrilateral are represented by the expressions 8x – 6 and 4x + 22. Find the length of a side of the quadrilateral.

8x – 6

4x + 22

8x – 6 = 4x + 22

4x – 6 = 22

4x = 28x = 7

Side Length = 8(7) – 6 = 50

Page 21: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

1.7 - Find Perimeter, Circumference, and Area

Page 22: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

Area:

Perimeter:

Square units inside a shape.

Measured in u2

cm2, in2, ft2

Length around a shape.

Measured in ucm, in, ft, yd

, yd2

Page 23: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

sP 4 2sA

Square:

s

Page 24: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

wA wP 22

Rectangle:

bhA

w

Page 25: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

cbaP bhA21

Triangle:

b

a ch

b

a ch

Page 26: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

rC 2 2rA

Circle:d

dC

Diameter = 2 radius

Page 27: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

1. Find the perimeter and area of the shaded figure.

sP 4 2sA )8(4P

inP 32

2)8(A264inA

Perimeter: _____________

Area: __________________

inP 32264inA

Page 28: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

1. Find the perimeter and area of the shaded figure.

298 ftA

Perimeter: _____________

Area: __________________

wP 22 bhA )7(2)14(2 P

1428PftP 42

)7)(14(A

ftP 42298 ftA

Page 29: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

1. Find the perimeter and area of the shaded figure.

cbaP bhA21

343016 PinP 80 )16)(30(

21

A

)16(15A2240inA

Perimeter: _____________

Area: __________________

inP 802240inA

Page 30: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

1. Find the perimeter and area of the shaded figure.

cbaP bhA21

204839 PcmP 107 )15)(48(

21

A

A 24(15)

A 360cm2

Perimeter: _____________

Area: __________________

cmP 107

A 360cm2

Page 31: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

2. Find the perimeter and area of the shaded figure.

Perimeter: _____________

Area: __________________

2rA dC )49(C

cmC 49 224.5A

A 600.25cm2

A 600.25cm2

cmC 49

Page 32: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

1. Find the perimeter and area of the shaded figure.

cbaP bhA21

13107 PmP 30 )5)(10(

21

A

)5(5A225mA

Perimeter: _____________

Area: __________________

mP 30225mA

Page 33: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

4. Use the information about the figure to find the indicated measure.

Perimeter = 84ftFind the length. wP 22

)13(2284 26284

258 ft29

Page 34: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

Area = 432m2

Find the width.

4. Use the information about the figure to find the indicated measure.

2A s2432 s

432 s

s 2 2 3 3 s 12 3m

Page 35: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

Area = 189cm2

Find the height.

4. Use the information about the figure to find the indicated measure.

bhA21

h)21(21189

189 10.5h

hcm 18

Page 36: 1.6 – Classify Polygons. Polygon: Plane figure that is formed by 3 or more segments, called sides such that: 1. Each side intersects exactly 2 other sides,

HW Problem

# 40a (hexagon)

1.6

1.7

44-47

52-56

1-13 odd, 14, 15-27 odd, 37, 40(a only), 41

1-15 odd, 27-29, 34-37, 41

Ans: 6 sides, 9 diagonals

**Bring ALL supplies tomorrow for review


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