Download 5.5 Inequalities Involving TWO Triangles

5.5 Inequalities Involving TWO
Triangles
What you’ll learn:
1. To apply the SAS Inequality
2. To apply the SSS Inequality
Theorem 5.13
SAS Inequality/Hinge Theorem
If 2 sides of a triangle are congruent to 2 sides of
another triangle and the included angle in one
triangle has a greater measure than the included
angle in the other, then the 3rd side of the 1st
triangle is longer than the 3rd side of the 2nd
E
triangle. B
If AB=DE and AC=DF
F
and A>D, then
A
C
D
BC>EF
Theorem 5.14
SSS Inequality
if 2 sides of a triangle are congruent to 2 sides of
another triangle and the 3rd side in one triangle is
longer than the 3rd side in the other, then the angle
between the pair of congruent sides in the 1st
triangle is greater than the corresponding angle in
the 2nd triangle.
E
A
If AB=DE, AC=EF, and
D
B
BC<EF, then A<B
C
F
Write an inequality relating the given
pair of angles or segment measures.
1.
15
20
D
A
50
B
15
C
P
2.
8
Q
S
6
AB _______ CD
4
4
R
mPQS ______ mRQS
Write an inequality describe the possible
values of x.
1.
3x-3<33
60 cm
36 cm
33
(3x-3)
60 cm
30 cm
and 3x-3>0
3x<36
3x>3
x<12
x>1
1<x<12
(½x -6)
2.
30
52
30
12
28
½x-6<52 and ½x-6>0
½x<58
½x>6
x<115
x>12
12<x<115
Given: CDAB,
mACB+mBCD<mABC+mCBD
AC=BD
Prove: AB<CD
1. CDAB,
mACB+mBCD<m
ABC+mCBD
AC=BD
2. BC=BC
3. ABC=BCD
4. mACB+mABC<m
ABC+mCBD
5. mACB<mCBD
6. AB<CD
A
B
1. Given
2.
3.
4.
5.
6.
C
Reflexive
Alt. int. angles 
substitution
Subtraction
SAS Inequality
D
Homework
p. 271
10-20 all, 34-40 even, skip 38