1. 5-4 The Triangle Inequality

2. Triangle Inequality Theorem: The sum of two lengths in a triangle is always greater than the third length. Aulisio cut to program…

3. Check It ! In ∆XYZ, XY=8, & XZ=14. Which measure cannot be YZ ? A 6B 10 C 14D 18

4. Remember: the shortest segment between a line and a point not on that line is perpendicular.

5. EXAMPLE: two measures of the sides of a triangle are 7 and 9. Give the possible range of the third side. Let’s call the third side “s” Sooo, s + 7 > 9 and s + 9 > 7 and 9 + 7 > s s > 2s > -216 > s The range has to satisfy all three of these conditions

6. s > 2s > -216 > s What is the ONLY way to satisfy these two conditions? s > 2 and s < 16 2 < s < 16

7. SHORTCUT! When finding the range of measure for a missing third side, just subtract the given measures to get the low end, and add them to get the high end ! Try it: Find the range of for the measure of the third side of a triangle given the measure of two sides. 12 and 18 < s <630