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.