Parallel Lines and Transversals TRANSVERSAL S A Transversal

Parallel Lines and Transversals

TRANSVERSAL S A Transversal is a line, ray, or segment that intersects two or more coplanar lines, rays, or segments, each at a different point

INTERIOR AND EXTERIOR INTERIOR – represented by the area inside the lines. EXTERIOR – represented by the area outside the lines.

MEASURING THE ANGLES E A 3 C F 5 7 8 6 1 4 D 2 B In the figure at the left AB CD with transversal EF. Measure all of the angles 1 – 8 using your protractor and record the measurement below. m 1= ______ m 2= ______ m 3= ______ m 4= ______ m 5= ______ m 6= ______ m 7= ______ m 8= ______

VERTICAL ANGLES E A 3 C 5 7 8 F 6 1 4 D 2 B List the names of vertical angle. What do you notice about the measures? Vertical Angle Theorem: if two angles form a pair of vertical angles, then they are _______________

CORRESPONDING List the pairs of ANGLESE corresponding angles. A 3 C F 5 7 8 6 1 4 D 2 B What do you know about their measures? Corresponding Angle Corresponding Postulate: If two lines angles are two non cut by a transversal are -adjacent angles, ____________ one interior and then corresponding one exterior that angles are lie on the same side of a ____________ transversal

ALTERNATE INTERIOR ANGLES E A 3 C F 5 7 8 6 Alternate Interior angles are two nonadjacent interior angles that lie on opposite sides of a transversal. 1 4 D 2 B List the pairs of alternate interior angles What do you notice about their measures? Alternate Interior Angles Theorem: If two lines cut by a transversal are ___________ then alternate interior angles are ___________

ALTERNATE EXTERIOR ANGLESE List the pairs of alternate A 3 C F 5 7 8 6 1 4 D 2 B external angles. What do you notice about their measures? Alternate Exterior Theorem: If two lines angles are two cut by a transversal are nonadjacent ___________ exterior angles then alternate exterior that lie on opposite sides of a angles are transversal ___________

SAME SIDE INTERIOR ANGLES E A 3 C 1 4 D 2 B List the pairs of same side interior angles. What do you notice 7 8 F about their measures? Same Side Interior Angles Theorem: If Same Side Interior two lines cut by a angles are two transversal are interior angles ___________ that line on then the same side of a interior angles are transversal. ___________ 5 6

SAME SIDE EXTERIOR List the pairs of same ANGLESE A 3 C F 5 7 8 1 6 Same Side Exterior angles are two exterior angles that lie on the same side of a transversal. 4 D 2 B side exterior angles. What do you notice about their measures? Same Side Exterior Angles Theorem: If two lines cut by a transversal are ___________ then same side exterior angles are ___________

Your Turn!!! For each pair below indicate the type of angles formed. l 1 2 3 4 5 7 8 6 a. ) Angles 1 and 5 b. ) Angles 3 and 6 c. ) Angles 4 and 8 d. ) Angles 2 and 7 e. ) Angles 4 and 6 m n

Your Turn!!! 1 2 3 4 5 7 8 In the figure at the left m 3= m 6= 6 Find: a. ) b. ) All of the angles 1 – 8

Your Turn!!! A D In the figure to the left DE BC, m DAE = 92 m DCB = 44 m DBC = 22 E C B Find: a. ) m b. ) m c. ) m d. ) m ADE = EDB = CDE =

SUMMARIZING ACTIVITY Take a moment to reflect on today’s lesson. In your notebook write a summary of what you have learned today.