Parallel and Perpendicular Lines

Parallel and Perpendicular Lines Perpendicular lines are two lines that intersect to form a 90º angle

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 l m

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 ll DC, AD ll BC, and EH ll FG

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

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

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

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 3 4 5 6 7 8 l m n

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

Transversal Mini-Lab (what do you already know?) Angles 1 and 2 are supplementary angles and must equal 180º 1 2 3 4 5 6 7 8 l m n

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 3 4 5 6 7 8 l m n

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 3 4 5 6 7 8 l m n

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

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

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

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 1 2 3 4 5 6 7 8 l m n

Congruent Angles with Parallel Lines Checkpoint Measure Concept 1 65° Given 2 115° Supplementary with 1 3 Vertical with 1 4 Vertical with 2 5 Corresponding with 1, Alt. Interior with 3 6 Corresponding with 2, Alt. Interior with 4 7 Corresponding with 3, Alt. Exterior with 1, Vertical with 5 8 Corresponding with 4, Alt. Exterior with 2, Vertical with 6 1 2 3 4 5 6 7 8 l m n

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

Congruent Angles with Parallel Lines and Equations 1 = 11x°, 6 = 5x° + 100° 11x° + 5x° + 100° = 180° 16x° + 100° = 180° 16x° = 80° x° = 5° Angle Measure Concept 1 55° Supplementary with 6, 11(5) = 55 2 125° Corresponding with 6 3 Vertical with 1 4 Vertical with 2 5 Corresponding with 1, Alt. Interior with 3 6 Supplementary with 1, 5(5) + 100 = 125 7 Corresponding with 3, Alt. Exterior with 1, Vertical with 5 8 Corresponding with 4, Alt. Exterior with 2, Vertical with 6 1 2 3 4 5 6 7 8 l m n

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