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Lesson 4-2 Angles of Triangles Ohio Content Standards: Ohio Content Standards: Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others. Ohio Content Standards: Make and test conjectures about characteristics and properties (e.g., sides, angles, symmetry) of twodimensional figures and threedimensional objects. Theorem 4.1 Angle Sum Theorem Theorem 4.1 Angle Sum Theorem The sum of the measures of the angles of a triangle is 180. Find the missing angle measures. 43° 79° 1 74° 2 3 Theorem 4.2 Third Angle Theorem Theorem 4.2 Third Angle Theorem If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangles are congruent. Exterior Angle Exterior Angle Angle formed by one side of a triangle and the extension of another side. Exterior Angle Angle formed by one side of a triangle and the extension of another side. 1 Remote Interior Angles Remote Interior Angles Interior angles of the triangle not adjacent to a given exterior angle. Remote Interior Angles Interior angles of the triangle not adjacent to a given exterior angle. 2 3 Theorem 4.3 Exterior Angle Theorem Theorem 4.3 Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. Find the measure of each numbered angle in the figure. 5 4 3 38° 32° 2 41°64° 1 29° Find mA if mC is 20. B 20° A C Assignment: Pgs. 189-191 11-35 all, 56-58 evens