Transcript section 3.5-3.8 - Fulton County Schools

3.5-3.8
By: Alex Melnick and Brian Yoon
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°
Given:
C
4 1 5
ABC
Prove: angle 1 + angle 2 + angle 3
=180°
Statement
ABC
2
A
L // AB
3
B
angle1+ angle4
+ angle5 = 180°
angle 2 = angle 4
angle 3 = angle 5
Reason
Given
Parallel Postulate
3 angles form a line
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
3.7- Mid-segments of
triangles and trapezoids
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
x2-x1
3 – (-3)
2–5
6
-3
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
Midpoint Formula
• The Midpoint of a segment with endpoints
(x1, y1) and (x2, y2) has the following
coordinates:
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 midsegment?
• No.
More Math Fun:
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