Section 14 2 Transversals and Parallel Lines 1
![Section 14. 2: Transversals and Parallel Lines 1 Section 14. 2: Transversals and Parallel Lines 1](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-1.jpg)
![Objective: By following instructions, students will be able to: 1. Prove and use theorems Objective: By following instructions, students will be able to: 1. Prove and use theorems](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-2.jpg)
![Def: transversal – A line that intersects two or more coplanar lines at different Def: transversal – A line that intersects two or more coplanar lines at different](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-3.jpg)
![Def: Corresponding Angles – angles that lie on the same side of the transversal Def: Corresponding Angles – angles that lie on the same side of the transversal](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-4.jpg)
![Def: Alternate Exterior Angles – angles that lie outside r and s on opposite Def: Alternate Exterior Angles – angles that lie outside r and s on opposite](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-5.jpg)
![Def: Alternate Interior Angles – angles that are non adjacent, lie between lines r Def: Alternate Interior Angles – angles that are non adjacent, lie between lines r](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-6.jpg)
![Def: Same-side interior angles– lie on the same side of the transversal and between Def: Same-side interior angles– lie on the same side of the transversal and between](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-7.jpg)
![Explain A List all pairs of angles that fit the description a) Corresponding b) Explain A List all pairs of angles that fit the description a) Corresponding b)](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-8.jpg)
![Explain B Given that , find each measure. State the reasoning. a) b) c) Explain B Given that , find each measure. State the reasoning. a) b) c)](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-9.jpg)
![explain 1 Prove the Alternate Interior Angles Theorem. Given: p ‖ q Prove: m∠ explain 1 Prove the Alternate Interior Angles Theorem. Given: p ‖ q Prove: m∠](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-10.jpg)
![Your-Turn #1 Suppose the measure of angle 4 is 57°. Describe two different ways Your-Turn #1 Suppose the measure of angle 4 is 57°. Describe two different ways](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-11.jpg)
![explain 2 Prove the Corresponding Angles Theorem. Given: p ‖ q Prove: m∠ 4 explain 2 Prove the Corresponding Angles Theorem. Given: p ‖ q Prove: m∠ 4](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-12.jpg)
![explain 3 A Find each value. Explain how to find the values using postulates, explain 3 A Find each value. Explain how to find the values using postulates,](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-13.jpg)
![explain 3 B Find each value. Explain how to find the values using postulates, explain 3 B Find each value. Explain how to find the values using postulates,](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-14.jpg)
![Your-Turn #2 In the diagram of a gate, the horizontal bars are parallel and Your-Turn #2 In the diagram of a gate, the horizontal bars are parallel and](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-15.jpg)
![Revisit Objective: Did we… 1. Prove and use theorems about angles formed by transversals Revisit Objective: Did we… 1. Prove and use theorems about angles formed by transversals](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-16.jpg)
![HW: Sec 14. 2 pg 515 #s 1 -15, 22 17 HW: Sec 14. 2 pg 515 #s 1 -15, 22 17](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-17.jpg)
- Slides: 17
![Section 14 2 Transversals and Parallel Lines 1 Section 14. 2: Transversals and Parallel Lines 1](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-1.jpg)
Section 14. 2: Transversals and Parallel Lines 1
![Objective By following instructions students will be able to 1 Prove and use theorems Objective: By following instructions, students will be able to: 1. Prove and use theorems](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-2.jpg)
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 Def: transversal – A line that intersects two or more coplanar lines at different](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-3.jpg)
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 Def: Corresponding Angles – angles that lie on the same side of the transversal](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-4.jpg)
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 Def: Alternate Exterior Angles – angles that lie outside r and s on opposite](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-5.jpg)
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 Def: Alternate Interior Angles – angles that are non adjacent, lie between lines r](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-6.jpg)
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 Sameside interior angles lie on the same side of the transversal and between Def: Same-side interior angles– lie on the same side of the transversal and between](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-7.jpg)
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 Explain A List all pairs of angles that fit the description a) Corresponding b)](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-8.jpg)
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 Explain B Given that , find each measure. State the reasoning. a) b) c)](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-9.jpg)
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 explain 1 Prove the Alternate Interior Angles Theorem. Given: p ‖ q Prove: m∠](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-10.jpg)
explain 1 Prove the Alternate Interior Angles Theorem. Given: p ‖ q Prove: m∠ 3 = m∠ 5 10
![YourTurn 1 Suppose the measure of angle 4 is 57 Describe two different ways Your-Turn #1 Suppose the measure of angle 4 is 57°. Describe two different ways](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-11.jpg)
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 explain 2 Prove the Corresponding Angles Theorem. Given: p ‖ q Prove: m∠ 4](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-12.jpg)
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 explain 3 A Find each value. Explain how to find the values using postulates,](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-13.jpg)
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 explain 3 B Find each value. Explain how to find the values using postulates,](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-14.jpg)
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
![YourTurn 2 In the diagram of a gate the horizontal bars are parallel and Your-Turn #2 In the diagram of a gate, the horizontal bars are parallel and](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-15.jpg)
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 Revisit Objective: Did we… 1. Prove and use theorems about angles formed by transversals](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-16.jpg)
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 HW: Sec 14. 2 pg 515 #s 1 -15, 22 17](https://slidetodoc.com/presentation_image/58c7cb38e1fab492aae0e73f45565eb4/image-17.jpg)
HW: Sec 14. 2 pg 515 #s 1 -15, 22 17
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