5-2: Inequalities and Triangles. Compare Angle Measures Compare m<3 to m<1 and m<2. Exterior Angle Inequality Theorem: The measure of any exterior angle.

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Presentation transcript:

5-2: Inequalities and Triangles

Compare Angle Measures Compare m<3 to m<1 and m<2. Exterior Angle Inequality Theorem: The measure of any exterior angle of a triangle is greater than the measures of its two corresponding remote interior angles.

EX 1: Find all angles whose measures are less than m<8. EX 2: Find all angles whose measures are greater than m<2.

Geometer’s Sketchpad Demonstration: What are some other ways that we can tell which angle has the greatest measure? What do the lengths of the sides have to do with the angles?

Sides and Angles The biggest side is across from the biggest angle, and the smallest side is across from the smallest angle.

EX 3: m<DAB_____ m<ABD EX 4: m<CDB _____ m<CBD EX 5: m<CDA _____ m<CBA

EX 6: Name the longest side. If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer.

Practice: p. 251; )Never 2)Varies 3)Grace 4)<2 5)<3 6)<3 7)<4, <5, <6 8)<1, <7 9)<2, <3, <4, <5 10)m m<XYW 11)m<XZY < m<XYZ 12)m<WX < m<XWY 13)AE<EB 14)CE>CD 15)BC=EC

Assignment: Honors: –P. 252; 17-34, Regular: Workbook 5-2