By: Alex Melnick and Brian Yoon

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3.5-3.8

• By Alex Melnick and Brian Yoon

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3.5 Triangle Sum Theorem

• The Parallel Postulate Given a line and a point
  not on the line, there is one and only one line
  that contains the give point and is parallel to
  the given line
• Triangle Sum Theorem The sum of the measures of
  the angles of a triangle is 180

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Given ABC Prove angle 1 angle 2 angle
3 180
C
4
5
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Statement Reason
ABC Given
L // AB Parallel Postulate
angle1 angle4 3 angles form a line
angle5 180 angle 2
angle 4 angle 3 angle 5
2
3
A
B
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• 3.6-Angles in polygons

Polygon Types Concave-1 or more angles are
pointed inwards Convex- All angles face outwards.
Shape Sides Sum of interior angles One interior angle
Triangle 3 180 60
Square 4 360 90
Pentagon 5 540 108
Hexagon 6 720 120
Heptagon 7 900 128.6
Octagon 8 1080 135
N-gon N 180(N-2) 180(N-2) N
The sum of the exterior angles of all polygons
are 360
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3.7- Mid-segments of triangles and trapezoids
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3.8 Analyzing Polygons With Coordinates

• Definition of slope The slope of a nonvertical
  line that contains the points(x1, y1) and (x2,
  y2)is equal to y2-y1
• 
  x2-x2
• Ex. Find the slope of AB with the endpoints
  A(5,-3) and B(2,3)
• y2-y1 3 (-3) 6
• x2-x1 2 5 -3

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3.8 cont.Parallel and Perpendicular Lines

• Parallel Line Theorem Two nonvertical lines are
  parallel if and only id they have the same slope.
  Any two vertical lines are parallel
• Perpendicular Lines Theorem Two nonvertical
  lines are perpendicular if and only if the
  product of their slopes is -1. Any vertical line
  is perpendicular to any horizontal line

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Midpoint Formula

• The Midpoint of a segment with endpoints (x1, y1)
  and (x2, y2) has the following coordinates

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Quiz

• The sum of the angles in a regular polygon is
  34,020, how many sides does the polygon have?
• 191
• If one angle of a right triangle is 86 what are
  the measurements of the other two angles?
• 4 and 90
• The base of a triangle is 279.36 and a segment
  that is inside of the triangle is 138.18, is this
  the mid-segment?
• No.

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More Math Fun

• HERE!!

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