1. Parallel and Perpendicular Lines

2. Perpendicular lines are two lines that intersect to form a 90 degree angle

3. Parallel and Perpendicular Lines Parallel lines are two lines that, if extended indefinitely, would never cross or touch In the figure below, line l is parallel to line m ( l // m ) l m

4. Parallel and Perpendicular Lines Checkpoint Name all sets of parallel line segments in each of the figures below: ab e f dc hg Lines AB and DC, AD and BC, and EH and FG

5. Parallel and Perpendicular Lines Checkpoint Name all sets of perpendicular line segments in each of the figures below: ab e f dc hg Lines AD and DC, DC and BC, AB and BC, AB and AD, EH and GH, and GH and FG

6. Transversals A line that intersects two other lines is called a transversal In the figure below, l || m and n is the transversal Eight angles are formed when a transversal intersects two parallel lines 1 2 3 4 5 6 7 8 l m n

7. Transversal Mini-Lab For this mini-lab, you will need: Notebook paper Pencil Two colored pencils (share with neighbor) Ruler (share with neighbor) Protractor

8. Transversal Mini-Lab 1.Draw two parallel lines using the lines on your notebook paper. 2.Using a ruler, draw any line (not perpendicular) to intersect these two parallel lines. 3.Label the angles formed using the numbers 1 – 8 as shown below: 12 34 56 78 l m n

9. Transversal Mini-Lab 4.Use a protractor to measure each angle and record it’s measurement below your figure (example: m 2 = 28 degrees) 5.Shade angle 1 and each angle that has a congruent measurement with a colored pencil. 6.Shade angle 2 and each angle that has a congruent measurement with another colored pencil. 7.Compare your results with a neighbor and be prepared to discuss

10. Transversal Mini-Lab (what do you already know?) Angles 1 and 2 are supplementary angles and must equal 180 degrees 12 34 56 78 l m n

11. Transversal Mini-Lab (what do you already know?) Angles 1 and 3 and angles 2 and 4 are vertical angles that have the same measure. 12 34 56 78 l m n

12. Congruent Angles with Parallel Lines The symbol means congruent to If a pair of parallel lines is intersected by a transversal, pairs of congruent angles are formed 12 34 56 78 l m n

13. Congruent Angles with Parallel Lines Congruent angles formed in between the parallel lines are known as alternate interior angles 4 6 and 3 5 12 34 56 78 l m n

14. Congruent Angles with Parallel Lines Congruent angles formed outside of the parallel lines are known as alternate exterior angles 1 7 and 2 8 12 34 56 78 l m n

15. Congruent Angles with Parallel Lines Congruent angles formed in the same position on the two parallel lines in relation to the transversal are known as corresponding angles 1 5; 2 6; 3 7; and 4 8 12 34 56 78 l m n

16. Congruent Angles with Parallel Lines Checkpoint In the figure below, m 1 = 65 Explain how you find the measure of each of the rest of the angles using vocabulary words such as supplementary, vertical, corresponding, alternate interior, and alternate exterior angles 12 3 4 5 6 7 8 l m n

17. Congruent Angles with Parallel Lines and Equations In the figure below, m 1 = 11x m 6 = 5x + 100 Find the value of x and then find the measure of the remaining angles 1 2 3 4 5 6 78 l m n Hint: Angles 2 and 6 are Corresponding and angles 1 and 2 are Supplementary

18. Homework Skill 2: Parallel and Perpendicular Lines (both sides) Practice 6-1: Line and Angle Relationships (both sides) Due Tomorrow!