Topic: Parallel Lines Date: 2010 Objectives: SWBAT…. Determine the angle pair relationship when given two parallel lines cut by a transversal Calculate the missing angle measurements when given two parallel lines cut by a transversal Calculate the missing angle measurements when given two intersecting lines and an angle

Parallel Lines What are Parallel Lines? Parallel lines are lines that lie in the same plane and do not intersect. A B C D Symbol Form: AB II CD

Angles and Parallel Lines A transversal is a line that intersects two other lines in two different points. Note that 8 angles are formed. A B 1 2 3 4 C D 5 6 7 8

ACTIVITY Determine Angle Relationships formed by Parallel Lines Cut by Transversal 1 2 3 4 5 6 7 8

S T O P !!!! Distribute transparency sheets, parallel lines and record sheet for activity

Interior and Exterior Angles B 1 2 3 4 Interior C D 5 6 7 8 Exterior Interior angles are angles between the parallel lines Exterior angles are angles outside the parallel lines

Alternate Interior Angles B 3 4 C D 5 6 Alternate Interior Angles are equal if two parallel lines are cut by a transversal So 3 and 6 are alternate interior angles And they are CONGRUENT and 4 and 5 are alternate interior angles

Alternate Exterior Angles B 1 2 C D 7 8 Alternate Exterior Angles are equal if two parallel lines are cut by a transversal So 2 and 7 are alternate exterior angles And they are CONGRUENT and 1 and 8 are alternate exterior angles

Corresponding Angles A B C D When two lines are cut by a transversal, 4 pairs of corresponding angles are formed. A B 1 2 3 4 C D 5 6 7 8 Corresponding angles are congruent!

Vertical Angles Vertical angles are always equal. And – you will always have vertical angles wherever two lines intersect! A B 1 2 3 4 C D 5 6 7 8

Interior Angles on the Same Side are Supplementary B 3 4 C D 5 6 m4 + m6 = 180 m3 + m5 = 180

Exterior Angles on the Same Side are Supplementary B 1 2 C D 7 8 m1 + m7 = 180 m2 + m8 = 180

Adjacent Angles creating a straight line are Supplementary B 2 4 C D 7 8 m2 + m4 = 180 m7 + m8 = 180

Now how do we apply these Angle relationships? B C D 1 2 3 4 5 6 7 8 m 3 = 40˚. Find the m 5. Explain how m 1 = 125˚. Find the m 8. Explain how m 7 = 38˚. Find the m 4. Explain how you determined your answer

Summary Alternate Interior Angles are equal Alternate Exterior Angles are equal Corresponding Angles are equal Vertical Angles are equal Interior Angles on the same side are supplementary Exterior Angles on the same side are supplementary Adjacent Angles creating a straight line are supplementary

Algebraic Applications Problem 1 In the accompanying diagram, l ll m. Find the measure of the angle represented by (5x – 30) (3x + 40) (5x – 30) l m SOLUTION: The two angles are corresponding angles, so they are congruent Set up the equation 3x + 40 = 5x - 30 and solve for x (x = 35) Once you know the value of x, substitute this value for x in 5x – 30 5(35) – 30 = 145

Algebraic Applications Problem 2 In the accompanying diagram, l ll m. Find the measure of the angle represented by (5x – 30) (5x – 10) (4x + 1) p q a SOLUTION: (x – 10) and a are corresponding angles, so they are congruent But, first, we need to find the value of x 4x + 1 and 5x – 10 form a straight angle, so they are supplementary. Set up the equation 4x + 1 + 5x – 10 = 180 and solve for x (x = 21) Once you know the value of x, substitute this value for x in 5x – 10 5(21) – 10 = 95 Since a is congruent, we know a = 95.