2.5
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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 - PowerPoint PPT PresentationTRANSCRIPT
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2.5
How Can See It?Pg. 20
Classify Polygons
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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.
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2.28 –EXTERIOR ANGLE OF TRIANGLES a. Compare the interior and exterior angle of the following triangles at right. What do you notice?
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70°
55°
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ba
c d
a+b+c = 180
Exterior Angle of a Triangle
c+d = 180a+b+c = c+d
a+b = d
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ba
c d
Sum of two interior angles equals exterior angle
Exterior Angle of a Triangle
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b. Find the measure of the exterior angles.
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50 + 70 = x120 = x
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5x + 45 = 6x + 3045 = x + 3015 = x
6(15) + 30
120°
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Polygon:
2. No sides overlap3. No curved sides
1. Has at least 3 sides
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Side: Line segment forming the polygon
M
T
SR
Q
QM
MT
TS
SR
RQ
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Vertex: Point where two sides meet
M
T
SR
Q
MTS
R
Q
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Consecutive Sides: Two sides that share a point, one after the other
M
T
SR
Q
and MTQM
and QRQM
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Diagonal: Segment that joins two nonconsecutive sides M
T
SR
Q
QT
QS
MS
MR
TR
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# of sides Name345
trianglequadrilateral
pentagon
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# of sides Name3456789
101112n
trianglequadrilateral
pentagonhexagonheptagonoctagon
nonagondecagon
11-gondodecagonn-gon
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Convex: No corners point inside the shape
Concave: Not convex! A corner points inside the shape
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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, _________________
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1. State whether the shape is a polygon. If yes, is it concave or convex? If no, why not?
Yes, Concave or ConvexOR
No, _________________
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1. State whether the shape is a polygon. If yes, is it concave or convex? If no, why not?
Yes, Concave or ConvexOR
No, _________________
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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
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Equilateral Equiangular Regular
All sides are congruent
All angles are congruent
All sides AND all angles are congruent
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2. Classify the name of the polygon by the number of sides. Is the polygon equilateral, equiangular, regular, or neither?
Equilateral
Pentagon
a.
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b.
Regular
quadrilateral
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c.
Equiangular
Octagon
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d.
Regular
Heptagon
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e.
equilateral
decagon
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f.
neither
Hexagon
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3. Given the following shapes are regular, solve for x.
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10x – 27 = 6x + 174x – 27 = 17
4x = 44x = 11
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x2+12x–106 = x2–6x–1618x – 106 = –16
18x = 90x = 5
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x2+8 = x2+2x–28 = 2x – 2
10 = 2x5 = x