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Transcript 
Angles in Triangles
April 21, 2015
What's Going On?
Naming Angles
iPad Investigation
Exit Card
Learning Goal ­ I will determine the angle relationships in triangles and be able to problem solve with them .
1
Angles in Triangles
April 21, 2015
Determine the measure of angle x.
Justify. (include all theorems used)
x
38o
2
Angles in Triangles
April 21, 2015
Unit 5: Geometric Relationships
Today's Topic
Angle Relationships
in Triangles
3
Angles in Triangles
April 21, 2015
Naming Angles
X
A
Z
B
C
Y
4
Angles in Triangles
April 21, 2015
iPad Investigation
5
Angles in Triangles
April 21, 2015
What is the sum of the
angles in a triangle?
180
o
6
Angles in Triangles
April 21, 2015
What is the sum of the angles in a triangle?
o
180
ALWAYS
This is actually a theorem... our first theorem!
The Interior Angle Theorem (IAT)
The sum of the interior angles of any triangle
is always 180o .
7
Angles in Triangles
April 21, 2015
Theorems
Interior Angle Theorem (IAT)
Find the measure of angle X.
To find the measure of an interior angle given two interior angles:
23o
X
39o
1. Start with 180o.
2. Subtract each angle.
3. What remains is the measure of the missing angle.
8
Angles in Triangles
April 21, 2015
Theorems
Supplementary Angle Theorem (SAT)
What's are supplementary angles?
A
supplementary angles are
two angles that exist along
a straight line
X
B
Y
Z
C
A and X
B and Y
C and Z
9
Angles in Triangles
April 21, 2015
Theorems
Supplementary Angle Theorem (SAT)
supplementary angles are two angles that
exist along a straight line
A
X
What is the sum of two
supplementary angles?
B
Y
Z
C
10
Angles in Triangles
April 21, 2015
Theorems
Supplementary Angle Theorem (SAT)
The sum of two supplementary angles is 180o.
A
X
A + X = 180o
B + Y = 180o
C + Z = 180o B
Y
Z
C
11
Angles in Triangles
April 21, 2015
Theorems
What about the
exterior angles of a triangle?
A
X
B
Y
Z
C
12
Angles in Triangles
April 21, 2015
A
X
We know that
180o
180o
180o
(A + X) + (B + Y) + (C + Z) = 540o
SAT
SAT
SAT
B
Y
Z
C
AND
X + Y + Z = 180o SATT
So...
A + X + B + Y + C + Z = 540o If we remove X, Y and Z we are taking away 180o worth of angles.
What do we have left? We only have A, B and C left (the exterior angles!)
And we have to take 180o from 540o...
540o - 180o = 360o
13
Angles in Triangles
April 21, 2015
Theorems
The Exterior Angle Theorem (EAT)
The sum of the exterior angles of a
triangle is always 360o.
A
X
o
A + B + C = 360
B
Y
Z
C
14
Angles in Triangles
April 21, 2015
15
Angles in Triangles
April 21, 2015
New Terms
Opposite Angles
Transversal
Alternate Angles
Corresponding Angles
Co­Interior Angles
Interior Angle
Exterior Angle
Supplementary Angles
16
Angles in Triangles
April 21, 2015
New Theorems
Opposite Angle Theorem
Alternate Angle Theorem
Corresponding Angle Theorem
Co­Interior Angle Theorem
Interior Angle Theorem
Supplementary Angle Theorem
Exterior Angle Theorem
17
Angles in Triangles
April 21, 2015
Exit Card
18
Angles in Triangles
April 21, 2015
Exit Question
D
A
x
E
Find the measure of angle x. State any and all theorems you use.
67o 29o B
C
F
19
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