obj. 12 proving lines parallel
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Prove lines are parallelTRANSCRIPT
- 1. Obj. 12 Proving Lines ParallelThe student is able to (I can): Use angles formed by a transversal to show that lines areparallel.
2. Recall that the converse of a theorem isfound by exchanging the hypothesis andconclusion.The converses of the parallel line theoremscan be used to prove lines parallel Corresponding Angles Alternate Interior Angles Alternate Exterior Angles If angles are congruent, then the linesare parallel. Same-Side Interior Angles If angles are supplementary, then thelines are parallel. 3. Example Find values of x and y that make the redlines parallel and the blue lines parallel.(x40) (x+40)If the blue lines are parallel, then the same-sideinterior angles must be supplementary.x 40 + x + 40 = 1802x = 180x = 90y 4. Example Find values of x and y that make the redlines parallel and the blue lines parallel.(x40) (x+40)If the red lines are parallel, then the same-sideinterior angles must be supplementary.90 40 + y = 18050 + y = 180y = 130y 5. Given: bisects DBA; 3 @ 1Prove:BECD BECB2 31D E APlan of proof: Because bisects DBA,BE2 @ 3. Because 3 @ 1,I can set 2 @1 usingsubstitution. 1 and 2 arealternate interior angles, andsince they are congruent, thelines are parallel. 6. Given: bisects DBA; 3 @ 1Prove:BECD BECB2 31D E ASSSSttttaaaatttteeeemmmmeeeennnnttttssss RRRReeeeaaaassssoooonnnnssss1. B E bisects DBA 1. Given 7. Given: bisects DBA; 3 @ 1Prove:BECD BECB2 31D E ASSSSttttaaaatttteeeemmmmeeeennnnttttssss RRRReeeeaaaassssoooonnnnssss1. BEbisects DBA 1. Given2. 2 @ 3 2. Def. bisector 8. Given: bisects DBA; 3 @ 1Prove:BECD BECB2 31D E ASSSSttttaaaatttteeeemmmmeeeennnnttttssss RRRReeeeaaaassssoooonnnnssss1. BEbisects DBA 1. Given2. 2 @ 3 2. Def. bisector3. 3 @ 1 3. Given 9. Given: bisects DBA; 3 @ 1Prove:BECD BECB2 31D E ASSSSttttaaaatttteeeemmmmeeeennnnttttssss RRRReeeeaaaassssoooonnnnssss1. BEbisects DBA 1. Given2. 2 @ 3 2. Def. bisector3. 3 @ 1 3. Given4. 2 @ 1 4. Subst. prop. @ 10. Given: bisects DBA; 3 @ 1Prove:BECD BECB2 31D E ASSSSttttaaaatttteeeemmmmeeeennnnttttssss RRRReeeeaaaassssoooonnnnssss1. BEbisects DBA 1. Given2. 2 @ 3 2. Def. bisector3. 3 @ 1 3. Given4. 2 @ 1 4. Subst. prop. @5. 5. Conv. alt. int. sCD BE