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Download Rentel Lesson 5.5 Inequalities in Triangles - Mustang-Math
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Transcript
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. m1 m2 and m1 m3 3 2 1 Application Given the figure below, explain why Statements Reasons 1. m1 m3 1. 2. m1 m2 2. 3. m2 m3 3. m2 m3 . Theorem Theorem 5-10: If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side. If XZ XY , then mY mZ . 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. If mA mB, then BC AC. 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. XY YZ XZ YZ ZX YX ZX XY ZY 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 1. 3. 4. b+c>b a=b+c 5. a>b 5. 1. 2. 3. 2. 4. Midterm Review Given the figure below, name the type of angle pairs given. 1) 3 and 8 2) 4 and 6 3) 1 and 7 4) 2 and 7 5) 5 and 8 6) 4 and 5 Midterm Review Find m1 and m2. Justify each answer. 1) 2) 1 135° 2 Midterm Review Find x in the following polygon. 125 ° x ° 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).