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3.5 Parallel Lines and Triangles• Parallel Postulate
– Through a point not on a line, there is one and only one line parallel to the given line.
Triangle Angle-Sum Theorem
• The sum of the measures of the angles of a triangle is 180.
Using the Triangle Angle-Sum Theorem• What are the values of x and y in the diagram?
59 43 180x 102 180x
78x
180m ADB m CDE 180x y
78 180y 102y
Exterior Angle of a Polygon• An exterior angle of a polygon is an angle
formed by a side and an extension of an adjacent side.– For each exterior angle of a triangle, the two
nonadjacent interior angles are its remote interior angles.
Triangle Exterior Angles Theorem• The measure of each exterior angle of a
triangle equals the sum of the measures of its two remote interior angles.
1 2 3m m m
Using the Triangle Exterior Angle Theorem• What is the measure of angle 1?
1 80 18m 1 98m
Using the Triangle Exterior Angle Theorem• What is the measure of angle 2?
124 59 2m 2 65m
More Practice!!!!!
• Homework – p. 175 – 176 #9 – 19.