2. 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.
Angles
3. 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
4. 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
3
2
1 4
exterior
angle
remot
e
interio
r
angle
s m<1 + m<2 = m<4
21. D E
5 3
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.
Make A Triangle
Construct triangle DEF.
22. The sum of the lengths of any two sides of a
triangle is greater than the length of
the third side.
Triangle Inequality Conjecture
Add the two smallest sides; they MUST be
larger than the third side for the triangle
to be formed.
23. Make A Triangle
Can the following lengths form a triangle?
1.
4 mm
5 mm
10 mm
2.
2 ft
9 ft
13 ft
5.
10 mm
3 mm
6 mm
8.
8 m
7 m
1 m
9.
9 mm
2 mm
1 mm
12.
1 mm
5 mm
3 mm
3.
5 cm
cm
4 cm
𝟐
4.
7 ft
15 ft
ft
𝟏𝟑
6.
7 ft
7 ft
ft
𝟕
7.
10 mm
13 mm
mm
𝟓
10.
12 mm
22 mm
mm
𝟏𝟑
11.
7 mm
8 mm
mm
𝟏𝟐
24. In a triangle, if one side is longer than another
side, then angle opposite the longer side
is larger than the other.
Side-Angle Conjecture
25. Side-Angle
What’s the biggest side?
What’s the biggest angle?
What’s the smallest side?
What’s the smallest angle?
C
B A
b
a
c
b
B
a
A
