Proving Lines Are Parallel

HGEO:

Proving Lines Parallel

Workbook 3-9

Identifying Parallel Lines

• Converse of Corresponding Angles Postulate

• Parallel Postulate

• Alternate Exterior Angles Converse

• Consecutive Interior Angles Converse

• Alternate Interior Angles Converse

• Perpendicular Transversal Converse

Theorem 3.19

Converse of Corresponding Angles Theorem

If two lines are cut by a transversal so that corresponding angles are congruent, then the line are parallel.

Theorem 3.13

Parallel Postulate

If given a line and a point not on the line, then there exists exactly one line that is parallel to the given line.

Theorem 3.20

Alternate Exterior Angles Converse

If two lines in a plane are cut by a transversal so that a pair of alternate exterior angle are congruent, then the lines are parallel.

Theorem 3.22

Consecutive Interior Angles Converse

If two lines in a plane are cut by a transversal so that a pair of consecutive interior angle is supplementary, then the lines are parallel.

Theorem 3.22

Alternate Interior Angles Converse

If two lines in a plane are cut by a transversal so that a pair of alternate interior angles are congruent, then the lines are parallel.

Theorem 3.23

Perpendicular Transversal Converse

If two lines in a plane are perpendicular to the same line, then the lines are parallel.

Example 1

a.

 $\angle2\ \cong\ \angle8$  
b.
 $\angle3\ \cong\ \angle11$  
c.
 $\angle12\ \cong\ \angle14$  

Example 1

a. alternate interior angles;
 $a\parallel b$ ; Alternate Interior Angles Converse

b. corresponding angles;  $l\parallel m$  ; Converse if Corresponding Angles Theorem

c. alternate exterior angles;  $a\parallel b$  ; Alternate Exterior Angles Converse

CHECK

You try!!

a.   $\angle1\ \cong\ \angle15$ 

b.  $m\angle3\ +\ m\angle10\ =\ 180$  

c.  $\angle3\ \cong\ \angle5$  

Multiple Select

$$\angle1\ \cong\ \angle15$$  

• $$l\parallel m$$ ;Alternate Exterior Angles Converse

• $$n\parallel k$$   ;Alternate Exterior Angles Converse

• $$l\parallel m$$ ; Converse of Corresponding Angles Theorem

• It is not possible to determine whether the lines are parallel.