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Angles formed by Transversal and Parallel Lines March 3, 2010 Warm Up 3/3/10 1. Simplify: 5 3 36 4 7 2. Solve for m: 2 m 5 5 m 3 3. Solve for x: x 4 12 4. Multiply and simplify: 4 2 5. Simplify: 2 4 6 12 6 8 Warm Up 3/4/10 1. Estimate to the nearest tenth: 70 2. Find - 169 3. Simplify and subtract: 5 8 3 32 4. Find n: 8 2 7 8n 5. Write in standard form: 9.7 10-4 Parallel Lines Coplanar lines that do not intersect. m m || n n Skew lines are non-coplanar, non-intersecting lines. q p The Transversal t Any line that r intersects two or more coplanar s lines. When parallel lines are cut by a transversal… t r 1 2 4 3 5 7 Angle pair relationships are formed. 6 8 Some angle pairs are congruent and other s angle pairs are supplementary. Remember! • Congruent angles have the same measure. 2 3 • Supplementary Angles are angles that have a sum of 180 degrees. 2 8 180 Corresponding Angles t Corresponding angles are congruent angles on the same side of the transversal. r 1 2 4 3 5 7 6 8 s 1 5 List the other corresponding angles Alternate Interior Angles t Alternate Interior angles are congruent angles on opposite sides of the transversal and inside the parallel lines. r 1 2 4 3 5 7 6 8 s 3 6 List the other alternate interior angles. Alternate Exterior Angles t Alternate Exterior angles are congruent angles on opposite sides of the transversal and outside the parallel lines. r 1 2 4 3 5 7 6 8 s 2 7 List the other alternate exterior angles. Same Side Interior t Same side interior angles are supplementary angles on the same side of the transversal and inside the parallel lines. r 1 2 4 3 5 7 6 8 s 4 6 180 List the other same side interior angles. Same Side Exterior t Same side exterior angles are supplementary angles on the same side of the transversal and outside the parallel lines. r 1 2 4 3 5 7 6 8 s 2 8 180 List the other same side exterior angles. Vertical Angles t Vertical angles are congruent angles located diagonally opposite each other. r 1 2 4 3 5 7 6 8 s 2 3 List the other vertical angles. Angle 2 measures 110°. What do the other angles measure? 1. 2. 3. 4. 5. 6. 7. 8. 58 58 ˚˚ lr 2 3 458 ˚ 58˚ 585˚ lw 6 7 8 58˚ lr || lw If angle 1 = 58 ˚ then angle 5 = 58 ˚ because they are corresponding angles, which are congruent to each other Since angle 1 = 58 ˚ then angle 4 = 58 ˚ and since angle 5 = 58 ˚ then angle 8 = 58 ˚ because they are vertical angles, which are congruent to each other 58 ˚ lr 122˚ 2 3 122 ˚ 4 5 lw 6 ˚ 122 7 122˚ 8 lr || lw If angle 1 = 58 ˚ then angle 2 = 122 ˚ because the two angles form a line, which is equal to 180 ˚ Since angle 2 = 122 ˚ then angle 7 = 122 ˚ because they are Alternate Exterior angles, which are congruent to each other. Since angle 3 = 122 ˚ then angle 6 = 122 ˚ because they are Alternate Interior angles, which are congruent to each other. 2 lr 1 3 4 6 5 lw 8 7 lr || lw •Angles 3 and 4 are Same Side Angles, therefore, they are supplementary and add up to 180 degrees. •If angle 3 is 120 degrees, angle 4 must be 60 degrees. 7-2 Parallel and Perpendicular Lines In the figure, line l || line m. Find the measure of the angle. 4 m4 = 124° Course 3 7-2 Parallel and Perpendicular Lines In the figure, line l || line m. Find the measure of all the angles. Course 3 7-2 Parallel and Perpendicular Lines Warm Up In the figure a || b. 1. Name the angles congruent to 3. 1, 5, 7 2. Name all supplementary angels. 3. If m1 = 105° what is m3? 105° 4. If m5 = 120° what is m2? 60° Course 3 lr || lw lr || lw lr || lw lr || lw lr || lw Summary Question 3/3/10 Tell your neighbor: Name the two kinds of angles that are formed when a transversal line crosses two parallel lines. Summary Question 3/4/10 Tell your neighbor: If an angle measures 45 degrees, how can you find the measure of the angle adjacent (next) to it?