2.5
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Transcript of 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