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4-4: Proving Lines Parallel

4-4: Proving Lines Parallel. 4-4: Proving Lines Parallel. Postulate 4-2: If two lines are cut by a transversal, and corresponding angles are congruent, then the lines are parallel. 4-4: Proving Lines Parallel.

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4-4: Proving Lines Parallel

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  1. 4-4: Proving Lines Parallel

  2. 4-4: Proving Lines Parallel • Postulate 4-2: If two lines are cut by a transversal, and corresponding angles are congruent, then the lines are parallel.

  3. 4-4: Proving Lines Parallel • That postulate leads us to the following four conclusions. If two lines are cut by a transversal, and… • Theorem 4-5: alternate interior angles are congruent, or • Theorem 4-6: alternate exterior angles are congruent, or • Theorem 4-7: consecutive interior angle are supplementary • Theorem 4-8: those two lines are perpendicular to the same line • Then the lines are parallel

  4. 4-4: Proving Lines Parallel • Examples: Identify the parallel segments • In the letter Z • Because alternate interior angle(ABC and DCB) are equal, AB || CD (Theorem 4-5) • In the letter F • Because GA  RD and GA GY,GY || RD (Theorem 4-8)

  5. 4-4: Proving Lines Parallel • Find the value of x so a || b • In this case, the third linemust be a transversal • To be parallel, 3x would have to equal 105 as they are alternate exterior angles(Theorem 4-6) • 3x = 105x = 35 (divide by 3)

  6. 4-4: Proving Lines Parallel • Find the value of x so BE || TS • If BE is parallel to TS, thenES would be a transversal. • BES and TSE would then be consecutive interior angles, whose sum is 180˚ (Theorem 4-7) • (2x + 10) + (5x + 2) = 1807x + 12 = 180 (combine like terms)7x = 168 (subtract 12 both sides)x = 24 (divide by 7)

  7. 4-4: Proving Lines Parallel • Assignment • Worksheet #4-4

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