Triangle Sum Theorem. Draw a Triangle. Make sure your lines are dark!. Tear off two vertices…. Line up the 3 angles (all vertices touching). What do they make?. A straight line = 180°. Angle sum of a Triangle. 180 °
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Triangle Sum Theorem
Transcript
Triangle Sum Theorem
Draw a Triangle
Make sure your lines are dark!
Tear off two vertices….
Line up the 3 angles (all vertices touching)
What do they make?
A straight line = 180°
Angle sum of a Triangle 180 <1 + <2 + <3 = 180
1
2
3
ALWAYS!!!
Consider a Quadrilateral What is the angle sum?
<1 + <2 + <3 + <4 = ?
Quadrilateral Draw a diagonal…what do you
get?
Two triangles
1
2 3
4
5
6
Quadrilateral Each triangle = 180
Therefore the two triangles together = 360
1
2 3
4
5
6
180
180
Angle sum of a Quadrilateral 180 + 180 =
360
Consider a Pentagon What is the angle sum?
Pentagon Draw the diagonals from 1 vertex
How many triangles?
Angle sum of a Pentagon Draw the diagonals from 1 vertex
180
180
180
Continue this process through Decagon Draw the diagonals from 1 vertex
Continue this process through Decagon Draw the diagonals from 1 vertex
What about a 52-gon?
What is the angle sum? Sorry I can’t draw it.
Can you find the pattern?
Number of sides
Number of
triangles
Angle sum of polygon
3 1 180
4 2 360
5 3
6
7
8
Find the nth term
Number of sides
Number of
triangles
Angle sum of polygon
3 1 180
4 2 360
5 3
6
7
8
9
10
nth n
Exterior angle sum Now that you
can find the angle sum of a polygon, what about the exterior angle sum?
65
35
80
Exterior angle sum Note: Extend
each side of the triangle. This makes a LINEAR PAIR
65
35
80100
145
115
Exterior angle sum
Add up the exterior angles
100+145+115=
360
65
35
80100
145
115
Quadrilateral 100+80+55+125 = 360
100 125
80 55
8055
100125
Pentagon
72* 5 = 360
108
108
108
108
108 72
72
72
72
72
What conclusion can you come up with regarding the exterior angle sum of a CONVEX polygon??
The exterior angle sum of a CONVEX polygon =
360
Interior Angle Measure of a REGULAR polygons
60 90
Equilateral Triangle Angle measure = 60
Square Angle measure = 90
These are measurement that we generally know at this time,