 Same-Side Exterior Angles: Definition &amp - MywallpapersMobi

# Same-Side Exterior Angles: Definition &amp Show Ads
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# Alternate Exterior Angles

When two lines are crossed by another line (called the Transversal ):

Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.

 In this example, these are two pairs of Alternate Exterior Angles:a and hAndb and g To help you remember: the angle pairs are on Alternate sides of the Transversal, and they are on the Exterior of the two crossed lines.

## Parallel Lines

When the two lines being crossed are Parallel Lines the Alternate Exterior Angles are equal.

(Click on "Alternate Exterior Angles" to have them highlighted for you.)

Exterior Angles Transversal Parallel Lines and Pairs of Angles Vertical Angles Corresponding Angles Alternate Interior Angles Consecutive Interior Angles Angles On a Straight Line Angles Around a Point Degrees (Angle) Congruent Angles Geometry Index

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# Alternate Exterior Angles

When two lines are crossed by another line (called the Transversal ):

Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines but on opposite sides of the transversal.

 In this example, these are two pairs of Alternate Exterior Angles:a and hAndb and g To help you remember: the angle pairs are on Alternate sides of the Transversal, and they are on the Exterior of the two crossed lines.

## Parallel Lines

When the two lines being crossed are Parallel Lines the Alternate Exterior Angles are equal.

(Click on "Alternate Exterior Angles" to have them highlighted for you.)

Exterior Angles Transversal Parallel Lines and Pairs of Angles Vertical Angles Corresponding Angles Alternate Interior Angles Consecutive Interior Angles Angles On a Straight Line Angles Around a Point Degrees (Angle) Congruent Angles Geometry Index

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J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

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# Same Side Interior and Same Side Exterior Angles – Concept

Brian McCall ###### Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

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When two parallel lines are intersected by a transversal, same side interior (between the parallel lines) and same side exterior (outside the parallel lines) angles are formed. Since alternate interior and alternate exterior angles are congruent and since linear pairs of angles are supplementary , same side angles are supplementary.

parallel lines

angles

congruence

interior

exterior

transversal

If we apply what we know about Alternate Interior and Alternate Exterior angles, then we come up with some interesting things about same side angles. Now what do I mean about same side? Well same side Interior angles would be 4 and 5, so notice we have parallel lines and the transversal. 4 and 5 are on the same side of that transversal.
So if two parallel lines are intersected by a transversal then same side, I’ll say interior since this is in between angles are supplementary. But why do they have to be supplementary? Well if we look at what we know about alternate exterior, alternate interior angles we know they have to be congruent. And we know that 5 and 6 here have to be supplementary since they are a linear pair. Which means that 5+6 must be 180 degrees and since 6 and 4 are congruent then by the transitive property which means if 5 and 6 are supplementary then 5 and 4 are supplementary we can say that same side interior angles are supplementary.
The same thing applies for same side exterior angles, so I’m going to erase this and write exterior. But what am I talking about same side exterior, well if I erase these marks exterior means outside of the parallel lines. So if I chose angle two the same side exterior would not be 6 cause 6 is in between the parallel lines but it will be 7. So angle 2 and angle 7 are also supplementary same thing with angle 1 and angle 8. These two are on the same side and will be supplementary.

Geometry

Reasoning, Diagonals, Angles and Parallel Lines

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Angles on the Same Side of the Transversal
Definition

Angles on the same side of the transversal are angles that are in one of the half-planes formed by the transversal .

Usually this term is combined with interior or exterior angles to define "interior angles on the same side of the transversal" and "exterior angles on the same side of the transversal".

Examples

In each illustration below, LINE 1 is a transversal of LINE 2 and LINE 3. In each illustration below, the following angles are interior angles on the same side of the transversal:

• A and F
• D and G
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In each illustration below, LINE 1 is a transversal of LINE 2 and LINE 3. In each illustration below, the following angles are exterior angles on the same side of the transversal:

• B and E
• C and H
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Theorem

When a transversal intersects two lines, the two lines are parallel if and only if interior angles on the same side of the transversal and exterior angles on the same side of the transversal are supplementary (sum to 180°).

In illustration one of the example section above, LINE 1 and LINE 2 are parallel and both interior and exterior angles on the same side of the transversal are supplementary.

In illustration two of the example section above, LINE 1 and LINE 2 are NOT parallel and both interior and exterior angles on the same side of the transversal are NOT supplementary.

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