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5.5 Inequalities in Triangles. Can you figure out the puzzle below???. DOM. Domino. Comparison Property of Inequality. a. b. c. Comparison Property of Inequality: If a = b + c , and c > 0, then a > b. Theorem.
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5.5 Inequalities in Triangles Can you figure out the puzzle below??? DOM Domino
Comparison Property of Inequality a b c Comparison Property of Inequality: If a = b + c, and c > 0, then 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. 3 1 2
Application Given the figure below, explain why . Statements Reasons 1. 2. 3. 1. 2. 3.
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 Can you figure out the puzzle below??? HW 5.5: #1-25 (1st column), 32, 33, 35 p.192: #3-4, 11, 22, 24-26 ESGG SGEG GEGS SGGE Scrambled Eggs
Proof of Comparison Property of Inequality Given: a = b + c, c > 0 Prove: a > b Statements Reasons c > 0 b + c > b + 0 b + c > b 1. 2. 3. 4. 5. 1. 2. 3. 4. 5. 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) 1 135° 2
Midterm Review Find x in the following polygon. x° 125° 125°
Midterm Review Find the equation of a line that goes through the point (-2, 1) and (3,2). Find the equation of a line parallel to y + 3x = 5 that goes through the point (-3, 5).