Download topic 5-2: triangle inequalities

TOPIC 5-2: TRIANGLE INEQUALITIES
Use the straws and string to find out if a triangle can be made.
Sides
Could a
Classify by
Sum of >, <, or Larger
triangle be
Sides
shorter
=
side
made:
sides
Yes or No?
2
2
2
2
2
3
2
3
4
2
3
5
2
3
6
3
4
5
3
3
6
3
3
3
3
3
4
3
5
6
What did you find out ?
In order for a triangle to be constructed, the sum of the smaller sides must
be ______________________the larger side.
EXAMPLES: Determine if the following sides will make a triangle
and if yes, then classify by sides.
1. 8, 9, 10
yes or no
______________________
2. 1, 1, 2
yes or
no
______________________
3. 6, 6, 10
yes or
no
______________________
4. 3, 5, 7
yes or
no
______________________
5. 4, 4, 4
yes or
no
______________________
EXAMPLE 6: If two sides of a triangle are 3 and 7, what range of
numbers would be possible for the length of the third side?
EXAMPLE 7: If two sides of a triangle are 9 and 20, what range of
numbers would be possible for the length of the third side?
In a triangle the largest side is opposite the largest angle, and the
smallest side is opposite the smallest angle.
EXAMPLE 8:  A = 120,  B = 40, C = 20
B
Largest side:
C
A
Smallest side:
EXAMPLE 9
Classify the triangle by sides, then list the angles from small to large.
B
12
70
A
70
15
9
C
Classify:_________________
Angles:______, ______, ______
EXAMPLE 10
List the sides of ABC in order from longest to shortest if the angles
of ABC have the indicated measures: mA = (10x),
mB = (5x – 17), mC = (7x –1).