Geometry Notes
5.6 Inequalities in Two Triangles
Name____________
The Hinge Theorem:
If 2 sides of 1 ! are ! 2 sides of another ! , and the included angle of the 1st ! is larger
than the included angle of the 2nd ! , then the 3rd side of the 1st ! is _____________than
the 3rd side of the 2nd ! .
Converse of the Hinge Theorem:
If 2 sides of 1 ! are ! 2 sides of another ! , and the 3rd side the 1st ! is longer than the 3rd
side of the 2nd ! , then the included angle of the 1st ! is _____________than the included
angle of the 2nd ! .
Complete the following with >, <, or =
1. TP_____AG
2. m ! 1______m ! 2
3.DE______EF
4. m ! 1_______m ! 2
5. m ! 1______m ! 2
6. m ! 1______m ! 2
7. m ! DBF_____m ! ABF
C
4
6
2
7
9
12
1
2 12
A
1
8
B
10
8. m ! FDB_______m ! BDC
Write an inequality or pair of inequalities to describe possible values of x.
9.
10.
11.
6
F
9
8
D