1. Inequalities in 2 triangles
Section 5-7

2. The Hinge Theorem
The hinge theorem works by making the following assumptions
2 sides of both triangles are congruent
Does the door or the threshold change size when you open the door?
The angle in question (hinge angle) must be between the two known sides
The other two angles are harder to visualize
Keep it simple
The hinge angle must be between 0 and 180 degrees
The larger third side is related to the larger angle across from it
Last section
Now for a picture

3. The Hinge Theorem A F 67 C B 23 D E

4. NASTY EXAMPLE 1 Find the range of values for x
Track across
15 > 10
60 > 5x – 20
80 > 5x
16 > x
Since the variable was on the small side, must use the constraint 15 10 60
5x-20

5. Nasty Example 1 cont. Constraint Final Answer 5x – 20 > 0 + 20 + 20
5x > 20
x > 4
Final Answer
4 < x < 16

6. Nasty Example 2 Find the range of values for x
9 > 7
3x + 18 > 90
3x > 72
x > 24
Variable is on larger side
Apply the other constraint
How many degrees in a triangle? 9
3x + 18 7
90°

7. Nasty Example 2 cont. Constraint Final Answer 3x + 18 < 180
3x < 162
x < 54
Final Answer
24 < x < 54

8. Assignment
Pg 336 – 337
6 – 14
16 – 18