Parallel and Perpendicular Lines

1. Parallel and Perpendicular Lines

2. Parallel and Perpendicular Lines • Perpendicular lines are two lines that intersect to form a 90ºangle

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 ll m lm

4. Parallel and Perpendicular Lines Checkpoint • Name all pairs of parallel line segments in each of the figures below: a b e f d c h g AB llDC, AD llBC, and EH llFG

5. Parallel and Perpendicular Lines Checkpoint • Name all pairs of perpendicular line segments in each of the figures below: a b e f d c h g AD DC, DC BC, AB BC, AB AD, EH GH, and GH 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 l 4 3 5 6 m 8 7 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 • Draw two parallel lines using the lines on your notebook paper. • Using a ruler, draw any line (not perpendicular) to intersect these two parallel lines. • Label the angles formed using the numbers 1 – 8 as shown below: 1 2 l 4 3 5 6 m 8 7 n

9. Transversal Mini-Lab • Use a protractor to measure each angle and record it’s measurement below the figure (example: m 2 = 28º) • Shade angle 1 and each angle that has a congruent measurement with a colored pencil. • Shade angle 2 and each angle that has a congruent measurement with another colored pencil. • 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 180º 1 2 l 4 3 5 6 m 8 7 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. 1 2 l 4 3 5 6 m 8 7 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 1 2 l 4 3 5 6 m 8 7 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 1 2 l 4 3 5 6 m 8 7 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 1 2 l 4 3 5 6 m 8 7 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 1 2 l 4 3 5 6 m 8 7 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 n 1 2 l 4 3 5 6 m 8 7

17. Congruent Angles with Parallel Lines Checkpoint n 1 2 l 4 3 5 6 m 8 7

18. 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 Hint: Angles 2 and 6 are Corresponding and angles 1 and 2 are Supplementary 1 2 4 3 l 5 6 8 7 m n

19. Congruent Angles with Parallel Lines and Equations 1 = 11x°, 6 = 5x° + 100° 11x° + 5x° + 100° = 180° 16x° + 100° = 180° 16x° = 80° x° = 5° n 1 2 l 4 3 5 6 m 8 7

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