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

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Presentation transcript:

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

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

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.

Example 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.

5.5 Inequalities in Triangles HW 5.5: #1-25 (1st column), 32, 33, 35 p.192: #3-4, 11, 22, ESGG SGEG GEGS SGGE Can you figure out the puzzle below??? Scrambled Eggs

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

Midterm Review Given the figure below, name the type of angle pairs given.

Midterm Review Find. Justify each answer. 1) 2) 135° 1 2

Midterm Review Find x in the following polygon. 125° x°x°

Midterm Review Find the equation of a line parallel to y + 3x = 5 that goes through the point (-3, 5). Find the equation of a line that goes through the point (-2, 1) and (3,2).