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5.2. Proving that Lines are Parallel. A. B. C. D.  ACD is an exterior angle. A & B are remote interior angles. m  ACD is greater than m  A . m  ACD is greater than m  B. 2. 1. 3. 4. 5. 6. 8. 7. 1  2 PQ ║ RS PQR  RSP 3  4 QR ║ PS

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5.2

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5 2

5.2

Proving that Lines are Parallel


5 2

A

B

C

D

 ACD is an exterior angle. A & B are remote interior angles.

mACD is greater than mA.

mACD is greater than mB


5 2

2

1

3

4

5

6

8

7


5 2

1  2

PQ ║ RS

PQR  RSP

3  4

QR ║ PS

PQRS is a parallelogram.

Given

Alt. int. s  → ║ lines.

Given

Subtraction Property.

Same as 2.

A 4-sided figure with both pairs of opposite sides parallel is a parallelogram.


5 2

7 ways to prove lines parallel

  • AIP Alt Interior Angles ≅

  • CAP Corresponding Angles ≅

  • AEP Alt Ext Angles ≅

  • SSISP same side interior angles supp parallel lines

  • SSESP same side exterior angles supp parallel lines

  • 2p3p two lines in a plane are both perpendicular to the same line they are parallel

  • Transversal of parallel if 2 lines are both parallel to the same line then they are parallel


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