1. 1.4c: Lines and Angle Relationships -proving lines parallel GSE’s M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, M(G&M)–10–9 Solves problems off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope

2. Corresponding  s If 2 lines are cut by a transversal so that corresponding  s are , then the lines are . ** If  1   2, then l  m. lmlm 1 2

3. m n m n

4. Alt. Ext.  s Converse If 2 lines are cut by a transversal so that alt. ext.  s are , then the lines are . ** If  1   2, then l  m. lmlm 1 2

5. Consecutive Int.  s Converse If 2 lines are cut by a transversal so that consecutive int.  s are supplementary, then the lines are . ** If  1 &  2 are supplementary, then l  m. 1 2 lmlm

6. Alt. Int.  s Converse If 2 lines are cut by a transversal so that alt. int.  s are , then the lines are . ** If  1   2, then l  m. 1 2 lmlm

7. Ex: Based on the info in the diagram, is p  q ? If so, give a reason. Yes, alt. ext.  s conv. No p q p q p q

8. Ex: Find the value of x that makes j  k. The angles marked are consecutive interior  s. Therefore, they are supplementary. x + 3x = 180 4x = 180 x = 45 j k x o 3x o

9. Are there any parallel lines In this bookcase? How do you know?

11. Suppose that maple Street and Oak Street follow a straight line path and intersect Route 6 at angles 90º and 85º, as shown in the map below. If the streets continue in a straight line, will their paths ever cross?

12. Distance between a point & line The shortest distance between a point and A line is its perpendicular segment R V m The distance from Point R to line m is VR.

13. Draw the segment that would represent the distance from the point to the line. 1. 2. 3. 4.

14. Name the segment whose length represents the distance between the following points and lines. 1) A to BC 2) C to AB 3) B to AC 4) N to BC

15. Assignment