1. Lesson 5 – 6 Inequalities in Two Triangles
Geometry
Lesson 5 – 6
Inequalities in Two Triangles
Objective:
Apply the Hinge Theorem or its converse to make comparisons in
two triangles.
Prove triangle relationships using the Hinge Theorem or its converse.

2. Inequalities in Two Triangles
Hinge Theorem
If two sides of a triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle.

3. Converse of Hinge Theorem
If two sides of a triangle are congruent to two sides of another triangle, and the third side in the first triangle is longer than the third side in the second triangle, then the include angle measure of the first triangle is greater than the included angle measure in the second.

4. Compare the given measures
WX and XY
WX < XY

5. Compare the given measures
JK and MQ
JK > MQ

6. Compare the given measures
AD and BD
AD > BD

7. Real World Group A is farther from camp since the included angle is
Two groups of snowmobilers leave from the same base camp. Group A goes 7.5 miles due west and then turns 35 degrees north of west and goes 5 miles. Group B goes 7.5 miles due east then turns 40 degrees north of east and goes 5 miles. At this point, which group is farther from the base camp? Explain.
Group A is farther from camp
since the included angle is
larger than Group B.
Draw a picture:

8. Find the range of possible values for x.
Angle has to be greater than 0, but less than 180.
6x + 15 < 180
6x + 15 > 0
6x + 15 > 65
Don’t have to solve since
we already said has to be
greater than 65.
Double check each time!
6x < 165
6x > 50

9. Find the range of possible values for x.
Don’t have to solve since
we already said has to be
less than 141.
Double check each time!
9a < 126
9a > -15
a < 14

10. Find the range of possible values for x.
The length of a side
must be positive.
Do not need < 180
since 180 is for an angle
not a side, and side has
no limit on length.
5x + 2 < 47
5x + 2 > 0
5x < 45
5x > -2
x < 9

12. Homework
Pg – 8 all, 10 – 22 E, 38, 44 – 58 E