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.

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Presentation transcript:

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°

b a c d a+b+c = 180 Exterior Angle of a Triangle c+d = 180 a+b+c = c+d a+b = d

b a c d Sum of two interior angles equals exterior angle Exterior Angle of a Triangle

b. Find the measure of the exterior angles.

=x 120 = x

5x + 45 =6x = x = x 6(15) °

Polygon: 2. No sides overlap 3. No curved sides 1. Has at least 3 sides

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

Vertex: Point where two sides meet M T S R Q M T S R Q

Consecutive Sides: Two sides that share a point, one after the other M T S R Q

Diagonal: Segment that joins two nonconsecutive sides M T S R Q

# of sidesName triangle quadrilateral pentagon

# of sidesName n triangle quadrilateral pentagon hexagon heptagon octagon nonagon decagon 11-gon dodecagon n-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 Convex OR No, _________________

1. State whether the shape is a polygon. If yes, is it concave or convex? If no, why not? Yes, Concave or Convex OR No, _________________

1. State whether the shape is a polygon. If yes, is it concave or convex? If no, why not? Yes, Concave or Convex OR No, _________________

1. State whether the shape is a polygon. If yes, is it concave or convex? If no, why not? Yes, Concave or Convex OR No, ____________________ Overlaps

EquilateralEquiangularRegular 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 x – 27 = 17 4x = 44 x = 11

x 2 +12x–106 = x 2 –6x–16 18x – 106 = –16 18x = 90 x = 5

x 2 +8 = x 2 +2x–2 8 = 2x – 2 10 = 2x 5 = x