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 line must be a transversal
To be parallel, 3x would have to equal 105 as they are alternate exterior angles (Theorem 4-6)
3x = 105 x = 35 (divide by 3)

6. 4-4: Proving Lines Parallel
Find the value of x so BE || TS
If BE is parallel to TS, then ES would be a transversal.
BES and TSE would then be consecutive interior angles, whose sum is 180˚ (Theorem 4-7)
(2x + 10) + (5x + 2) = x + 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