1. 6.4 Triangle Inequalities

2. Angle and Side Inequalities  Sketch a good size triangle in your notebook (about a third of the page).  Using a ruler find the approximate length of each side (in inches or centimeters).  How is the largest side related to the largest angle?  How is the smallest angle related to the smallest side?

3. Name the angles in ascending order.

4. Name the longest side. 43 Name the shortest side. o o o

5. TRIANGLE INEQUALITY THEOREM  The sum of the lengths of any two sides of a triangle is greater than the length of the third side.  Is it possible for a triangle to have the following lengths? 3, 6, 8 10, 10, 0.5 3 + 6 = 9 > 83 + 8 = 11 > 66 + 8 = 14 > 3YES 0.5 + 10 = 10.5 > 10 10 + 10 = 20 > 0.5 YES

6. Get on your “ Thinking Caps ”  Can you think of three lengths that cannot make a triangle?

7. More Triangle Inequality Practice  The lengths of two sides of a triangle are 3 and 5. The length of the third side must be greater than and less than. 5 - 325 + 38

8. Put the following angles in ascending order.

9. Section 6.4 #17

10. PRACTICE MAKES PERFECT!  Page 221  #1 – 16

11. Extra Credit Opportunity (SAT style!)  What is the smallest integer, x, for which x, x + 5, and 2x – 15 can be the lengths of the sides of a triangle?  Hint: Use the Triangle Inequality Theorem