Download 5.2: Triangle Inequalities

5.2: Triangle Inequalities
What is an inequality?
For any real number, a>b iff
there is a positive number c
such that a=b+c
All Properties Still Hold!
Addition, Subtraction,
Multiplication, Division, Transitive
etc.
Theorem 5.8: If an angle is an
exterior angle of a triangle, then its
measure is larger than the measure
of either remote interior angle.
m4  m1
m4  m3
3
1
2
4
Name all the angles whose
measures are less than <14
Angles 4, 11, 9, 2, 3, 6, 7
Which angle is the largest?
Angle 1
Theorem 5.9: If one side of a
triangle is larger than a second
side, then the angle opposite that
side is larger than the angle
opposite the shorter side
Put the sides of the triangle in
order from smallest to largest
A
60
30
B
AB<BC<AC
C
Put the angles in order from
smallest to largest (assume x>0)
B
x-2
A
x+2
x
<C, <B, <A
C
Compare the following angles
1) m<RSU_____m<SUR
2) m<TSV_____m<STV
3) m<RSV_____m<RUV
It’s Proof Time!!
See Overhead