Triangle Sum Properties

1. 4.1 Triangle Sum Properties
October 14, 2013
Chapter 4: Congruent Triangles
Activity: Find the sum of the measures of the angles.
Materials: Paper, Ruler & Scissors
Draw 2 different sized triangles with one of the sides extended.
Label the 4 angles. Cut out the triangles.
A
W
B
C
D
X
Y
Z
1st Triangle: Tear off the three corners. Place them next to each
other on the extended line.
Make a conjecture about the sum of the measures of interior <s
2nd Triangle: Tear off corners that aren't next to the exterior <s.
Use them to fill the exterior <.
Make a conjecture about the relationship between the measure of
an exterior < and the nonadjacent interior <s.
Conclusions:
The sum of the measures of the interior <s of a triangle = 180.
The measure of the exterior angle of a triangle the sum of the 2
nonadjacent interior <s.
Oct 15­1:24 PM
HW pg. 221 #8­18 evens, 21­26, 32 & 36
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2. 4.1 Triangle Sum Properties
October 14, 2013
4­1 Triangle Sum Properties
Objectives:
To understand the sum of the measures of the angles of a
triangle.
Classify Triangles by Sides
Isosceles
Scalene
Equilateral
Classify Triangles by Angles
Acute
Right
Obtuse
Equiangular
Oct 15­1:30 PM
HW pg. 221 #8­18 evens, 21­26, 32 & 36
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3. 4.1 Triangle Sum Properties
October 14, 2013
Triangle Sum Theorem
The sum of the measures of the angles in every triangle is _____.
x = ______
xo
54o
39o
n = ______
no
135o
30o
Oct 17­9:52 AM
HW pg. 221 #8­18 evens, 21­26, 32 & 36
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4. 4.1 Triangle Sum Properties
October 14, 2013
Exterior Angle Theorem
The measure of an exterior < of a triangle = the sum of the measures of the 2
nonadjacent interior <s.
Exterior
Angle
Nonadjacent
Interior
Angles
2
1
3
Corollary to the Triangle Sum Theorem
The acute angles of a right triangle are complementary.
A
<A + <C = 90
B
C
Sep 20­12:46 PM
HW pg. 221 #8­18 evens, 21­26, 32 & 36
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5. 4.1 Triangle Sum Properties
October 14, 2013
Find the measure of each numbered angle in the figure.
3
2
50o
1
78 o
120 o
4
5
56o
109o
95o
1
2
33
o
3
24o
Sep 20­12:53 PM
HW pg. 221 #8­18 evens, 21­26, 32 & 36
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6. 4.1 Triangle Sum Properties
October 14, 2013
HW
pg. 221
#8­18 evens,
21­26, 32 & 36
Oct 13­7:13 AM
HW pg. 221 #8­18 evens, 21­26, 32 & 36
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