Download Triangle Inequalities

Triangle Inequalities
What makes a triangle and what type
of triangle
What makes a triangle
How do we know if the side lengths given could
be used to construct or draw a triangle
Pg 216 Investigation 1
The sum of the lengths of the two shorter sides
should be greater than the length of the longest
side.
Examples
Given sides do they make a triangle
3
5
8
No 3+5=8
3
5
9
No 3+5 <9
3
5
7
Yes 3+5>7
Angle and Side Relationship
How can you determine what side is the longest
given the angles or what angle is the largest
given the sides
Pg 217 Investigation 2
The longest sides is across from the largest angle
The largest angle is across from the longest side
Smallest angle across from shortest side
Shortest side across from the smallest angle
Example
Put sides in order from Longest to shortest
c
70
a
60
b,a,c
50
b
Put angles in order from largest to smallest
6
c
a
8
b
10
c,a,b
Exterior Angle of A triangle
What relationship do you notice about the
exterior angle of a triangle in relationship to the
interior angles
Pg 217 investigation 3
The exterior angle is equal to the sum of the two
remote interior angles
Remote interior angles are the two angles not
adjacent to the exterior angle
Example
Find the missing angle
x
X=60
115
55
X=120
55
65
x
How can the sides determine the type
of Triangle
How do we know if a triangle is a right triangle?
Pythagorean’s Theorem – a 2  b 2  c 2
where a and b are the shortest 2 sides and
c is the longest
2
2
2
Obtuse
a b  c
Acute
a b  c
2
2
2
Examples
4
6
8
Obtuse 16+36<64
5
8
9
Acute 25+64>81
6
8
10
Right 36+64=100
Homework
Pg 218
1-4 do the sides make a triangle and what kind
5,6,9,10,12,15,16
Honors 17