Angle Relationships in Parallel Lines and Triangles Module

Angle Relationships in Parallel Lines and Triangles Module 11

Review � Solving two step equations � 7 x + 9 = 30 --- The goal is to get the variable (x) ALONE! �Use reverse order of operations 7 x + 9 = 30 -9 -9 ______ 7 x = 21 ---- ---7 7 X =3

Naming Angles �You always names angles putting the vertex as the middle letter and use the angle symbol c a b < abc or <cba

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Angle Review �Complementary Angles: �Two angles whose measures add to 90˚ �Supplementary Angles: �Two angles whose measures add to 180˚

Vocabulary �Parallel lines: lines in a plane that do not intersect �Transversal: a line that intersects two lines in the same plane at two different points.

�What do you know about these angles? 1 2 exterior 3 4 5 6 �Vocab word: �Corresponding, alternate interior 7 exterior 8 interior, same side interior, alternate exterior, same side exterior, & vertical

� Vertical Angles: A pair of opposite Angles congruent angles formed by intersecting lines � <1 and <4, <2 and <3, <6 and <7, <5 and < 8 � Corresponding angles: lie on the same side of the transversal, on the same side of the parallel lines � <1 and <5, <2 and <6, <3 and <7, <4 and <8 � Alternate interior angles: non adjacent angles that lie on opposite sides of the transversal between the parallel lines � <3 and <6, <4 and <5 � Alternate Exterior Angles: lie on opposite sides of the transversal on the outside of the parallel lines. � <1 and <8, <2 and <7 � Same Side Interior Angles: lie on the same side of the transversal, between

Angles �Congruent angles have the same angle measure and its identified by the following symbol~ �Corresponding, vertical, and alternate interior and alternate exterior angles are congruent �So… �<1, <4, <5, <8 are congruent �<2, <3, <6, <7 are congruent

� If <1 = 65˚ what is the measure Angle Measures of <4? Justify? �<4 is 65 ˚ <1 and <4 are congruent because they are vertical angles � What is the angle measure of <3? Justify? �<3 is 115˚ because <1 and <3 are supplementary angles. Since <1 is ˚ 65˚, subtract that from 180 ˚ and get 115˚ � What is the angle measure of <8? Justify? �<8 is 65 ˚ because <1 and <8 are alternate exterior angles which are congruent.

Solve for a �Since <b + <a =180 ˚ � 3 x ˚ + 6 x ˚ = 180 b=6 x˚ a =3 x˚ � 9 x ˚ = 180 9 9 X =20 So 3 x ˚ = 3(20) ˚ = 60 ˚

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