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Parallel Lines and Transversals

Parallel Lines and Transversals. TRANSVERSALS. 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. EXTERIOR INTERIOR EXTERIOR.

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Parallel Lines and Transversals

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  1. Parallel Lines and Transversals

  2. TRANSVERSALS A Transversal isa line, ray, or segmentthat intersects two or more coplanar lines, rays, or segments, each at a different point

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

  4. MEASURING THE ANGLES E A 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= ______ 1 2 3 4 C D 5 6 7 8 F

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

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

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

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

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

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

  11. Your Turn!!! For each pair below indicate the type of angles formed. l 1 2 m 3 4 5 6 n 7 8 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

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

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

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

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