Download Inequalities in Two Triangles

INEQUALITIES IN TWO
TRIANGLES
Geometry CP1 (Holt 5-6)
K. Santos
Hinge Theorem (5-6-1)
If two sides of one triangle are congruent to two sides of
another triangle and the included angles are not congruent,
then the longer third side is across the larger included
angle.
B
E
A
If m<A > m<D
then BC > EF
C
D
F
Converse of the Hinge Theorem (5-6-2)
If two sides of one triangle are congruent to two sides of
another triangle and the third sides are not congruent, then
the larger included angle is across from the longer third
side.
H
L
G
J
K
If GH > KL
then m<J > m<N
N
Example—Comparing Sides
Compare: BC and AB
Given: m<ADB = 64° and
m<CDB = 65°
A
B
9
C
9
D
AD = CD
BD = BD
By using the Hinge Theorem
BC > AB
m<CDB >m<ADB
Example---Comparing angles
Compare: m<EGH and m<EGF
F
10
E
9
12
G
12
H
FG = HG
EG = EG
EF > EH
By the converse of the Hinge theorem
m<EGF > m<EGH