_____(0-10 pts) Describe the alternate exterior angles theorem and converse. Give at least 3 examples of each.

 

The Alternate Exterior Angles Theorem and its Converse:

 

When there are two parallel lines and they are cut by a transversal, two sections are formed. The interior, which is in between the two parallel lines, and the exterior, which is the outside of the two parallel lines. If two angles are on opposite sides of the transversal and on the exterior of the parallel lines, then these two angles are alternate exterior angles.

 

The Alternate Exterior Angles Theorem is:

• If 2 parallel lines are cut by a transversal, then any two alternate exterior angles are congruent. 

 

Its converse is this one:

 

The Alternate Exterior Angles Converse:

 

• If any two alternate exterior angles are congruent, then the two lines that are cut by a transversal are parallel. 

 

As you can notice, both of these statements are true, therefore the Alternate Exterior Angles Theorem is binconditional.

So the true theorem is:

 

• Two lines, that are cut by a transversal, are parallel if and only if (iff) any two alternate exterior angles are congruent.

 

 

EXAMPLES....

 

 

 

 

  

 

 

 

 

 

 

CONVERSE EXAMPLES... 

 

Example 1

Because <1 and <8 are alternate exterior angles and because they are congruent, the lines have to be parallel.

 

Example 2

Because <2 and <7 are alternate exterior angles, but they are not congruent, the lines cannot be parallel.

 

Example 3

 

Because <1 and <8 are alternate exterior angles and because they are congruent, the lines cut by the transversal are parallel.

 

_____(0-10 pts) Describe the consecutive interior angles theorem and converse. Give at least 3 examples of each.

 

Consecutive interior angles:

If two angles are located in the interior (between two lines) and are on the same side of the transversal they are consecutive interior angles, They can be on either side of the plane.

 

Converse: 

If they are consecutive interior angle,then they are 2 angles are located in the interior and are on the same side of the transversal.

 

  

 

Angles D and E  and c and f are consecutive interior because they are in the same place of the transversal, located in the interior.

 

 

 

 

Angles 4 and 6 and 3 and 5 are consecutive interior.

 

 

 

Angles 4 and 5 and 3 and 6 are consecutive interior.

 

Angles c and b and f and g are consecutive interior.

 

 

 

EXAMPLES....

 

 

 

 

CONVERSE EXAMPLES....

 

Example 1

Because <3 and <5 are consecutive interior angles and because they are supplementary, the lines have to be parallel.

 

Example 2

Because <4 and <6 are consecutive interior angles, but they are not supplementary, the lines cannot be parallel.

 

Example 3

 

Because <4 and <6 are consecutive interior angles and because they are supplementary, the lines cut by the transversal are parallel.