Download Angles in Triangles

1D Geometric Relationships ­ Day 1 (Angles in Triangles) ­ Student Input.notebook
November 16, 2012
What's Going On?
What Do We Know?
SATT, SAT, EAT
Exit Card
Learning Goal ­ I will be able to determine and describe the properties and relationships of the interior and exterior angles of triangles.
1
1D Geometric Relationships ­ Day 1 (Angles in Triangles) ­ Student Input.notebook
November 16, 2012
Unit 6: Geometric Relationships
Today's Topic
Angle Relationships
in Triangles
2
1D Geometric Relationships ­ Day 1 (Angles in Triangles) ­ Student Input.notebook
November 16, 2012
What Do We Know?
3
1D Geometric Relationships ­ Day 1 (Angles in Triangles) ­ Student Input.notebook
November 16, 2012
What Do We Know?
4
1D Geometric Relationships ­ Day 1 (Angles in Triangles) ­ Student Input.notebook
November 16, 2012
What Do We Know?
two sides are parallel
5
1D Geometric Relationships ­ Day 1 (Angles in Triangles) ­ Student Input.notebook
November 16, 2012
What Do We Know?
a
b
b
a
opposite
6
1D Geometric Relationships ­ Day 1 (Angles in Triangles) ­ Student Input.notebook
November 16, 2012
What Do We Know?
alternate
corresponding
co-interior
180o
7
1D Geometric Relationships ­ Day 1 (Angles in Triangles) ­ Student Input.notebook
November 16, 2012
What Do We Know?
What is the sum of the
angles in a triangle?
o
180
8
1D Geometric Relationships ­ Day 1 (Angles in Triangles) ­ Student Input.notebook
November 16, 2012
What is the sum of the angles in a triangle?
o
180
ALWAYS
This is actually a theorem... our first theorem!
The Sum of the Angles in a Triangle Theorem (SATT)
The sum of the interior angles of any triangle
is always 180o.
9
1D Geometric Relationships ­ Day 1 (Angles in Triangles) ­ Student Input.notebook
November 16, 2012
Theorems
Sum of the Angles in a Triangle Theorem (SATT)
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.
10
1D Geometric Relationships ­ Day 1 (Angles in Triangles) ­ Student Input.notebook
November 16, 2012
Theorems
Supplementary Angle Theorem (SAT)
What 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
11
1D Geometric Relationships ­ Day 1 (Angles in Triangles) ­ Student Input.notebook
November 16, 2012
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
12
1D Geometric Relationships ­ Day 1 (Angles in Triangles) ­ Student Input.notebook
November 16, 2012
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
Only one T!!
Does not require a Triangle
G
H
G and H are supplementary
13
1D Geometric Relationships ­ Day 1 (Angles in Triangles) ­ Student Input.notebook
November 16, 2012
Theorems
What about the
exterior angles of a triangle?
A
X
B
Y
Z
C
14
1D Geometric Relationships ­ Day 1 (Angles in Triangles) ­ Student Input.notebook
November 16, 2012
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
15
1D Geometric Relationships ­ Day 1 (Angles in Triangles) ­ Student Input.notebook
November 16, 2012
Theorems
The Exterior Angle Theorem (EAT)
The sum of the exterior angles of a
triangle is always 360o.
A
X
A + B + C = 360o
B
Y
Z
C
16
1D Geometric Relationships ­ Day 1 (Angles in Triangles) ­ Student Input.notebook
November 16, 2012
Exit Question
D
A
x
Find the measure of angle x. State any and all theorems you use.
We will do this on
Monday
E
67o 29o B
C
F
17
1D Geometric Relationships ­ Day 1 (Angles in Triangles) ­ Student Input.notebook
November 16, 2012
Homework
Pg. 371 - 372
# 1,2,4 (a, c)
3, 5 (a, c, e)
6, 9
18