Warm Ups Classify each angle Classify each angle Solve Each Equation x= x+105= x + 58 = x = 90

Chapter 3: Parallel Lines and the Triangle Angle-Sum Theorem Properties of parallel and perpendicular lines. Properties of parallel and perpendicular lines. Prove that lines are parallel. Prove that lines are parallel.

Triangle Angle-Sum Theorem The sum of the measure of the angles of a triangle is 180. The sum of the measure of the angles of a triangle is 180. A BC

Triangle Angle-Sum Theorem “The sum of the measures of the angles of a triangle is 180. “ Ex: A triangle has m<1=35 degrees and m<2=65 degrees. Find m<3. Ex: A triangle has m<1=35 degrees and m<2=65 degrees. Find m<3. Ex: Triangle MNP is a right triangle. <M is the right angle and m<N is 58. Find m<P. Ex: Triangle MNP is a right triangle. <M is the right angle and m<N is 58. Find m<P.

Find m Z m Z = 180Triangle Angle-Sum Theorem m Z = 180Simplify. m Z = 65Subtract 115 from each side. Parallel Lines and the Triangle Angle-Sum Theorem

m ACB = 90Definition of right angle c + 70 = 90Angle Addition Postulate c = 20Subtract 70 from each side. Find c first, using the fact that ACB is a right angle. In triangle ABC, ACB is a right angle, and CD AB. Find the values of a, b, and c. Parallel Lines and the Triangle Angle- Sum Theorem

a + m ADC + c = 180Triangle Angle-Sum Theorem m ADC = 90Definition of perpendicular lines a = 180Substitute 90 for m ADC and 20 for c. a = 180Simplify. a = 70Subtract 110 from each side m CDB + b = 180 Triangle Angle-Sum Theorem m CDB = 90 Definition of perpendicular lines b = 180 Substitute 90 for m CDB b = 180 Simplify. b = 20 Subtract 160 from each side. To find b, use CDB. To find a, use ADC. (continued) Parallel Lines and the Triangle Angle-Sum Theorem

Triangles Equiangular – all angles congruent Acute – all angles acute Right – one right angle Obtuse – one obtuse angle Equilateral – all sides congruent Isosceles – at least two sides congruent Scalene – no sides congruent

The three sides of the triangle have three different lengths, so the triangle is scalene. One angle has a measure greater than 90, so the triangle is obtuse. The triangle is an obtuse scalene triangle. Classify the triangle by its sides and its angles. Parallel Lines and the Triangle Angle- Sum Theorem

More Triangles Exterior Angle of a polygon is an angle formed by a side and an extension of an adjacent side. Exterior Angle of a polygon is an angle formed by a side and an extension of an adjacent side. Remote Interior Angles are the two nonadjacent interior angles for each exterior angle Remote Interior Angles are the two nonadjacent interior angles for each exterior angle

Triangle Exterior Angle Theorem The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles. The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles

Find m 1. m = 125Exterior Angle Theorem m 1 = 35Subtract 90 from each side. Parallel Lines and the Triangle Angle-Sum Thm

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