1. January 13-14 Vocab Quiz on Sections 5.1-5.4 Bell Ringer
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2. Corollary to the Triangle Exterior Angle Theorem
The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles. 3 2 1

3. Theorem 5.10
If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.

4. Theorem 5.11
If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle.
The longest side will be opposite the largest angle. The shortest side will be opposite the smallest angle.

5. Theorem 5.12 – Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

6. Using the Triangle Inequality Theorem
Can a triangle have sides with the given lengths?
3 ft., 7 ft., 8 ft.
3 + 7 > 8
10 > 8
3 + 8 > 7
11 > 7
7 + 8 > 3
15 > 3
Yes. The sum of the lengths of any two sides is greater than the length of the third side.

7. Using the Triangle Inequality Theorem
Can a triangle have sides with the given lengths?
b. 5 ft., 10 ft., 15 ft.
> 15
15 is not greater than 15.
No. The sum of 5 and 10 is not greater than 15.
This contradicts the Triangle Inequality Theorem.

8. Finding Possible Side Lengths
You have a triangular sandbox. Two of the sides are 5 ft. and 8 ft. long. What is the range of possible lengths for the third side?
x + 5 > 8
x > 3
x + 8 > 5
x > - 3
5 + 8 > x
x < 13
Numbers that satisfy x > 3 and x > -3 must be greater than 3. So, the third side must be greater than 3 ft. and less than 13 ft.

9. Hinge Theorem
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 from the larger included angle.

10. Converse of Hinge Theorem
Still need two sides congruent to two sides
If the 3rd side is longer, then the angle across from it is longer.

11. Example 1
Compare m∠BAC & m∠DAC

12. Example 2
Compare EF & FG

13. Example 3
Find the range of values for k.