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Geometry: Chapter 3. Ch. 3. 4: Prove Lines are Parallel Ch. 3.5 Using Properties of Parallel Lines. Postulate 16: Corresponding Angles Converse If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel.

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geometry chapter 3

Geometry: Chapter 3

Ch. 3. 4: Prove Lines are Parallel

Ch. 3.5 Using Properties of Parallel Lines

slide2
Postulate 16: Corresponding Angles Converse

If two lines are cut

by a transversal so

the corresponding

angles are congruent,

then the lines are parallel.

Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 161.

slide3
Ex. 1. Find the value of y that makes a || b.

Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 162.

slide4
Ex. 1 (cont.)

Solution: Lines a and b are parallel if the marked alternate exterior angles are congruent.

(5y +6)o =121o

5y=121-6

5y=115

y = 23

slide5
Theorem 3.8: Alternate Interior Angles Converse

If two lines are cut

by a transversal so the

alternate interior angles

are congruent, then the

lines are parallel.

Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 162.

slide6
Theorem 3.9: Consecutive Interior Angles Converse

If two lines are cut

by a transversal so the

consecutive interior

angles are supplementary,

then the lines are parallel.

Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 162.

slide7
Theorem 3.10: Alternate Exterior Angles Converse

If two lines are cut

by a transversal so the

alternate exterior angles

are congruent, then the

lines are parallel.

Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 162.

slide8
Example 2: A woman was stenciling this design on her kitchen walls. How can she tell if the top and bottom are parallel?

She can measure alternate interior angles or corresponding angles and see if they are congruent.

Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 162.

ex 3 prove that if 1 and 4 are supplementary then a b
Ex. 3: Prove that if 1 and 4 are supplementary, then a||b.

Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 163.

slide12
Theorem 3.11: Transitive Property of Parallel Lines.

If two lines are parallel to the same line, then they are parallel to each other.

slide13
Theorem 3.12: Lines Perpendicular to a Transversal Theorem

In a plane, if two lines are perpendicular to the same line, then they are parallel to one another.

If m┴ p and n┴ p,thenm || n.

Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 192.