Angle Relationships in Parallel Lines and Triangles Module 11
Review Solving two step equations 7x + 9 = 30--- The goal is to get the variable (x) ALONE! Use reverse order of operations 7x + 9 = 30 -9 -9 ____________ 7x = 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
Do page 344
Angle Review Complementary Angles: Supplementary Angles: Two angles whose measures add to 90˚ Supplementary Angles: Two angles whose measures add to 180˚ 22 ˚ 48 ˚
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? Vocab word: Corresponding, alternate interior, same side interior, alternate exterior, same side exterior, & vertical 1 2 exterior 3 4 5 6 interior 7 8 exterior
Angles Vertical Angles: A pair of opposite 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 the parallel lines <3 and <5, <4 and <6
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
Angle Measures If <1 = 65˚ what is the measure 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. Angle Measures
Solve for a b=6x˚ a =3x˚ Since <b + <a =180 ˚ 3x ˚ + 6x ˚ = 180 9 9 X =20 So 3x ˚ = 3(20) ˚ = 60 ˚
Page 350 #5-7 & Pg 351 #11-16