1. The Triangle Inequality Thm. & Inequalities Involving 2 Triangles Section 5-4 and 5-5

2. Triangle Inequality Thm. The sum of the lengths of any two sides of a triangle is greater than the length of the 3 rd side. A B C 6 7 10 AB + BC > AC

3. Theorem 5-12 The perpendicular segment from a point to a line is the shortest segment from the point to the line.. A B X Y

4. Corollary 5-1 The perpendicular segment from a point to a plane is the shortest segment from the point to the plane..

5. SAS Inequality (Hinge Thm.) If 2 sides of one triangle are congruent to 2 sides of another triangle, and the included angle in one triangle is greater than the included angle in the other, then the 3 rd side of the first triangle is longer than the 3 rd side in the 2 nd triangle.

6. 90 100 A B C D E F DF > AC

7. SSS Inequality If 2 sides of one triangle are congruent to 2 sides of another triangle and the 3 rd side in one triangle is longer than the third side in the other, then the angle between the pair of congruent sides in the first triangle is greater than the corresponding angle in the 2 nd triangle.

8. 10 12 A B C D E F Angle E > Angle B

9. Joke Time What would you say if someone took your playing cards? dec-a-gon

10. What kind of insect is good at math? an account-ant