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

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

Proof of Comparison Property of Inequality StatementsReasons Given: a = b + c, c > 0 Prove: a > b c > 0 b + c > b + 0 b + c > b a = b + c a > b

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?

Application Given the figure below, explain why. StatementsReasons

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

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

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

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.

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.

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.

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).

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.

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