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Theorem : If two parallel lines are cut by a transversal, the alternate interior angles are congruent.

Theorem: If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel.










Theorem: If two parallel lines are cut by a transversal, the alternate exterior angles are congruent. 

Theorem: If two lines are cut by a transversal and the alternate exterior angles are congruent, the lines are parallel. 





















vertical angles parallel lines
vertical angles parallel lines
video tutorial area of a parallelogram

Theorems associated with angles created by a transversal


Welcome to MooMooMath. Today we are going to talk to parallel lines cut by transversals. First of all we have two parallel lines over here. Line M and line N and they are drawn in blue and they are parallel to each other which means that don’t touch each other. Then we have this green line and we will call it line L and it is what we will call a transversal. It is a line that intersects both parallel lines. Now it c creates several relatiionships of angles. This video will touch on just one of these relelationships. Say we are given this angle.( Points to angle at the top) and angle one is 70 degrees and I will label the angle 70 degrees. We can figure out angle 2 and angle 3. Angle 2 is a vertical angle to angle one so that means that measure of angle two is also 70 degrees because vertical angles are congruent to each other. Now let’s look at angle three. Angle three is a linear pair with angle two. We know the measure of lines add up to 180 so if this angle is 70 the angle three will be it’s supplement so take 180 and subtract 70 and that equals 110 degrees. So angle three will be 110 degrees. Angle 1 and three are supplementary, angles two and three are also supplementary because angles 1 and angle 2 are congruent to each other so hope this video was helpful. 

Transversal Angles

vertical angles parallel lines
The angles<1 and <3 and <and<are vertical angles.
The angle measure of these angles are congruent.
In this picture angles <1 and <and <and <3 are linear pairs. The angle measure of linear pairs equals 180 degrees.
Interior
Exterior
Exterior
corresponding angles
alternate exterior angles
alternate interior angles
In this example <2 and < 6 and <5 and <3 are alternate interior angles
In this example <1 and < 8 and 
<4 and <7 are alternate exterior angles
In this example <4 and< 6,<3 and<8, <1 and <5, and <2 and<7 are corresponding angles
Transversal
line

Transversal Angles

Vertical angles are located opposite one another when two lines intersect. Vertical angles are congruent. They are called vertical angles because they share the same vertex.
In Geometry what are the properties of the angles created by transversals? A transversal is a line that intersects two or more lines that can be parallel. The transversal creates several angles. These angles are  given "names" that describe their location and properties. The following is a list of names with illustrations describing the angles created by transversals, as well as several theorems.
Three terms that will help with your understanding of angles related to transversals.

Interior means between the lines.
Exterior means outside the lines.
Alternate means on opposite sides of the transversal.


Linear Pairs of angles are located on corresponding sides of the transversal. They can be either interior or exterior angles. The angle measure of linear pairs add to 180, therefore they are supplementary.
Corresponding angles are found at the same location of  the lines that intersect. 
If the lines that are intersected by the transversal are parallel, then corresponding angles are equal measure. If the lines are not parallel, then there is no relationship between the angles.
alternate angles formed by transversal
Alternate angles are found on opposite sides of the transversal. They can be either interior alternate angles, or exterior alternate angles. Alternate angles are congruent if the intersected lines are parallel.
Angles and 8 are alternate exterior angles, and angles 3 and 5 are alternate interior angles.