1. 5.5 Inequalities in Triangles DOM Can you figure out the puzzle below??? Domino

2. Comparison Property of Inequality Comparison Property of Inequality: If a = b + c, and c > 0, then a > b. a b c

3. Proof of Comparison Property of Inequality StatementsReasons 1. 2. 3. 4. 5. 1. 2. 3. 4. 5. Given: a = b + c, c > 0 Prove: a > b c > 0 b + c > b + 0 b + c > b a = b + c a > b

4. Theorem 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. by the Δ Exterior Theorem. If we apply the comparison prop of inequality, what do we know?

5. Application Given the figure below, explain why. StatementsReasons 1. 2. 3. 1. 2. 3.

6. Theorem Theorem 5-10: If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.

7. Theorem List the angles of the following figure in order from smallest to largest.

8. Theorem Theorem 5-11: If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle.

9. Sides of a Triangle List the sides of the following triangle in order from shortest to longest. Determine which segment is shortest in the following diagram.

10. Theorem 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.

11. Theorem Can a triangle have sides with the given lengths? a) 7 ft, 3 ft, 8 ft b) 10 cm, 6 cm, 3 cm A triangle has sides of lengths 8 cm and 10 cm. Describe the lengths possible for the third side.

12. Lines Review Find the equation of the perpendicular bisector of the segment joined by points (3,2) and (-7, 4) in y = mx + b form. Find the equation of a line, in y = mx + b form, that goes through the points (-5, 4) and (5,6).

13. Lines Review Find the equations of the lines containing the midsegments of the triangle with vertices A(-3,2), B(5,6), and C(3,-4) in y = mx + b form.

14. 5.5 Inequalities in Triangles HW: p.292 #1-25 (x3), 32, 33, 37 ESGG SGEG GEGS SGGE Can you figure out the puzzle below??? Scrambled Eggs