1. Geometry Notes 2.2B – Solving Problems Applying Angle Properties of Lines LG.1.G.5 Explore, with and without appropriate technology, the relationship between angles formed by two lines cut by a transversal to justify when lines are parallel M.3.G.5 Identify and apply properties of and theorems about parallel and perpendicular lines to prove other theorems and perform basic Euclidean constructions

2. Review Using the diagram, solve for x. Steps 1.Classify the angles 2.Determine their relationship 3.Set up an equation 4.Solve for x (6x + 56) (3x - 20) rm d Given: m ll r

3. Now... What is the difference between the picture in the example and this picture? Have the angles changed? Has their relationship changed? (6x + 56) (3x - 20) r m d f

4. New Steps __________________ Classify the angles Determine their relationship Set up an equation Solve for x (6x + 56) (3x - 20) r m d f Extend your lines

5. Example Given that xy ll ef, solve for x Y X Z F E

6. Now You Try… Given that MN ll XY, solve for x. Y X Z M N (7x – 10)  (5x + 30) 

7. Other facts needed to complete homework: All 3 angles in any triangle sum to 180. Base angles of Isosceles triangles are congruent.

8. Parallelogram Given that MN ll XY & XM ll YN, solve for all missing angles.