Section 14 2 Transversals and Parallel Lines 1

Section 14. 2: Transversals and Parallel Lines 1

Objective: By following instructions, students will be able to: 1. Prove and use theorems about angles formed by transversals that intersect parallel lines. 2

Def: transversal – A line that intersects two or more coplanar lines at different points. Line t is the transversal to line r and line s. 3

Def: Corresponding Angles – angles that lie on the same side of the transversal t and on the same side of lines r and s. Theorem: If lines r and s are parallel and are cut by a transversal, then the pairs of corresponding angles are congruent. 4

Def: Alternate Exterior Angles – angles that lie outside r and s on opposite sides of the transversal. Theorem: If lines r and s are parallel and are cut by a transversal, then the pairs of alternate exterior angles are congruent. 5

Def: Alternate Interior Angles – angles that are non adjacent, lie between lines r and s, and are on opposite sides of the transversal. Theorem: If lines r and s are parallel and are cut by a transversal, then the pairs of alternate interior angles are congruent. 6

Def: Same-side interior angles– lie on the same side of the transversal and between the intersected lines. Postulate: If lines r and s are parallel and are cut by a transversal, then the pairs of same-side interior angles are supplementary. 7

Explain A List all pairs of angles that fit the description a) Corresponding b) Alternate Exterior c) Alternate Interior d) Consecutive Interior 8

Explain B Given that , find each measure. State the reasoning. a) b) c) d) 2) If and steps. , what is the value of x? Show your 9

explain 1 Prove the Alternate Interior Angles Theorem. Given: p ‖ q Prove: m∠ 3 = m∠ 5 10

Your-Turn #1 Suppose the measure of angle 4 is 57°. Describe two different ways to determine the measure of angle 6. 11

explain 2 Prove the Corresponding Angles Theorem. Given: p ‖ q Prove: m∠ 4 = m∠ 8 12

explain 3 A Find each value. Explain how to find the values using postulates, theorems, and algebraic reasoning. In the diagram, roads a and b are parallel. Explain how to find the measure of ∠VTU. 13

explain 3 B Find each value. Explain how to find the values using postulates, theorems, and algebraic reasoning. In the diagram, roads a and b are parallel. Explain how to find the measure of ∠WUV. 14

Your-Turn #2 In the diagram of a gate, the horizontal bars are parallel and the vertical bars are parallel. Find x and y. Name the postulates and/or theorems that you used to find the values. 15

Revisit Objective: Did we… 1. Prove and use theorems about angles formed by transversals that intersect parallel lines? 16

HW: Sec 14. 2 pg 515 #s 1 -15, 22 17