WARM - UP
What is a vertical angle?
 What are adjacent angles?
 What are supplementary angles?
 What are complementary angles?

EXTERIOR ANGLES
Angles

When the sides of a polygon are extended,
other angles are formed.

The original angles are the interior angles.

The angles that form linear pairs with the
interior angles are the exterior angles.
EXTERIOR ANGLE THEOREM
An exterior angle of a triangle…
… is equal in measure to the sum of the
measures of its two remote interior angles.
remote
interior
angles
Exterior angle
EXTERIOR ANGLE THEOREM
(YOUR NEW BEST FRIEND)
The measure of an exterior angle in a
triangle is the sum of the measures of the
2 remote interior angles
remote
interior
angles
exterior
angle
2
1
3
4
m<1 + m<2 = m<4
EXTERIOR ANGLE THEOREM
m∠1 = m∠A + m∠B
EXAMPLES
m<FHG = 180 – 111 = 69
m<G = 60 + 69
linear pair
EXAMPLES
Find x & y
y = 30 + 82
y = 112˚
82°
30°
x
y
x = 68°
y = 112°
180 = 30 + 82 + x
180 = 112 + x
68˚ = x
EXAMPLES
Find mJKM
2x – 5 = x + 70
x – 5 = 70
x = 75
m< JKM = 2(75) - 5
m< JKM = 150 - 5
m< JKM = 145˚
EXAMPLES
Solve for y in the diagram.
Solve on your own
before viewing the
Solution
SOLUTION
4y + 35 = 56 + y
3y + 35 = 56
3y
= 21
y= 27
EXAMPLES
Find the measure of 1 in the diagram shown.
Solve on your own
before viewing the
Solution
SOLUTION
40 + 3x = 5x - 10
40
= 2x - 10
50
= 2x
25 = x
m < 1= 5x - 10
m < 1= 5(25) - 10
m < 1= 125 - 10
m < 1= 115
CHECKPOINT: COMPLETE THE EXERCISES.
SOLUTION
Right Scalene triangle
x + 70 = 3x + 10
70 = 2x + 10
60 = 2x
30 = x
3 (30) + 10 = 100˚
TRIANGLE INEQUALITIES
Make A Triangle
Construct triangle DEF.
D
D
F
E
F
E
Make A Triangle
Construct triangle DEF.
D
D
F
E
F
E
Make A Triangle
Construct triangle DEF.
D
E
Make A Triangle
Construct triangle DEF.
D
E
Make A Triangle
Construct triangle DEF.
D
E
Make A Triangle
Construct triangle DEF.
5
3
D
E
13
Q: What’s the problem with this?
A: The shorter segments can’t reach each other to
complete the triangle. They don’t add up.
Triangle Inequality Conjecture
The sum of the lengths of any two sides of a
triangle is greater than the length of
the third side.
Add the two smallest sides; they MUST be
larger than the third side for the triangle to
be formed.
Make A Triangle
Can the following lengths form a triangle?
1.
4 mm
5 mm
10 mm
2.
5.
10 mm
3 mm
6 mm
6.
9.
9 mm
2 mm
1 mm
2 ft
9 ft
13 ft
3.
5 cm
𝟐 cm
4 cm
4.
7 ft
15 ft
𝟏𝟑 ft
7 ft
7 ft
𝟕 ft
7.
10 mm
13 mm
𝟓 mm
8.
10.
12 mm
22 mm
𝟏𝟑 mm
11.
7 mm
8 mm
𝟏𝟐mm
12.
1 mm
5 mm
3 mm
8m
7m
1m
Side-Angle Conjecture
In a triangle, if one side is longer than another
side, then angle opposite the longer side
is larger than the other.
Side-Angle
C
b
a
B
What’s the biggest side?
What’s the biggest angle?
What’s the smallest side?
What’s the smallest angle?
c
b
B
a
A
A
Side-Angle
Rank the sides from greatest to least.
46°
b
a
42°
92°
b
c
a
c
Rank the angles from greatest to least.
A
7
B
4
5
C
C
A
B