Geometry Lesson 5 3 Inequalities in One Triangle

Geometry Lesson 5 – 3 Inequalities in One Triangle Objective: Recognize and apply properties of inequalities to the measures of the angles of a triangle. Recognize and apply properties of inequalities to the relationships between the angles and sides of a triangle.

Definition of Inequality For any real number a and b, a > b if and only if there is a positive number c such that a = b + c If 5 = 2 + 3, then 5 > 2 and 5 > 3

Properties of Inequalities Comparison Property l a < b, a > b, or a = b Transitive Property If a < b and b < c, then a < c l If a > b and b > c, then a > c l Why does reflexive and symmetric not work? Addition property l If a > b, then a + c > b + c same for < Subtraction property l If a > b, then a - c > b - c same for <

Remember… Exterior Angle Theorem Exterior Angle: 1 Remote interior angles: 2 & 3

Exterior Angle Theorem The measure of an exterior angle of a triangle is greater than the measure of either of its corresponding remote interior angles.

Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition. Angles 1 & 2 since they are the Remote interior angles to angle 5 Angle 8 is an exterior angle of triangle JKL.

Angles 4 & 11 are remote interior angles to angle 14 Angle 9 is vertical to angle 11 Angles 3(with angle 4) and 2 are RI angles to angle 14 Angles 7, 8, 1 are remote interior to angle 15 (vert to 14) All exteriors angles with angle 5 being a R. I. angle

Angle-Side Inequalities Draw a scalene triangle ABC, give lengths for the sides. List the sides in order from least to greatest. List the angles in order from least to greatest.

Angle-Side Relationships in Triangles Theorem 5. 9 l If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side. Theorem 5. 10 l If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.

List angles and sides in order from smallest to largest.

List the sides from shortest to longest 79 39

Homework Pg. 346 1 – 7 all, 8 – 38 E, 46, 54, 56, 60