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Angles and Parallel Lines starrkingschool.net Topical synopsis | Geometry synopsis | MathBits" Teacher sources Terms of Use contact Person: Donna Roberts

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as soon as a transversal intersects two or an ext lines in the exact same plane, a collection of angles room formed. Details pairs of angles space given particular "names" based top top their areas in relationship to the lines. These details names may be supplied whether the lines connected are parallel or no parallel.

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Alternate internal Angles: The native "alternate" method "alternating sides" of the transversal.

You are watching: If 2 parallel lines are cut by a transversal then

This name clearly describes the "location" of this angles. As soon as the lines room parallel, the steps are equal.
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∠1 and also ∠2 are alternative interior angle ∠3 and ∠4 are alternate interior angles

alternating interior angles space "interior" (between the parallel lines), and also they "alternate" political parties of the transversal. Notification that they room not surrounding angles (next to one one more sharing a vertex).

When the lines are parallel, the alternate interior anglesare same in measure. m∠1 = m∠2 and also m∠3 = m∠4


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If you attract a Z on the diagram, the alternate interior angles deserve to be discovered in the corners that the Z. The Z may additionally be backward:
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If two lines are reduced by a transversal and also the alternate interior angles room congruent, the lines are parallel.
Alternate Exterior Angles: The indigenous "alternate" method "alternating sides" that the transversal. The name clearly describes the "location" of these angles. When the lines space parallel, the measures are equal.

alternative exterior angles are "exterior" (outside the parallel lines), and they "alternate" political parties of the transversal. Notice that, favor the alternating interior angles, these angles room not adjacent.

When the lines are parallel, the alternative exterior angles space equal in measure. m∠1 = m∠2 and m∠3 = m∠4


If two lines are cut by a transversal and the alternative exterior angles space congruent, the lines space parallel.
Corresponding Angles: The surname does not clearly describe the "location" of these angles. The angles space on the same SIDE that the transversal, one INTERIOR and one EXTERIOR, but not adjacent. The angles lie on the very same side the the transversal in "corresponding" positions. once the lines are parallel, the procedures are equal.
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∠1 and ∠2 are equivalent angles ∠3 and ∠4 are matching angles ∠5 and also ∠6 are matching angles ∠7 and ∠8 are matching angles

If friend copy one of the corresponding angles and you interpret it along the transversal, it will certainly coincide v the other matching angle. For example, slide ∠ 1 down the transversal and it will coincide v ∠2.

When the lines are parallel, the equivalent angles room equal in measure. m∠1 = m∠2 and also m∠3 = m∠4 m∠5 = m∠6 and m∠7 = m∠8


If you draw a F on the diagram, the matching angles have the right to be uncovered in the corners the the F. The F may also be backward and/or upside-down:
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If two lines are cut by a transversal and the equivalent angles are congruent, the lines space parallel.
Interior angles on the exact same Side the the Transversal: The surname is a description of the "location" that the these angles. once the lines are parallel, the steps are supplementary.
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∠1 and also ∠2 are inner angles top top the exact same side that transversal ∠3 and also ∠4 are internal angles on the exact same side of transversal

this angles are located specifically as their name describes. They room "interior" (between the parallel lines), and they space on the same side of the transversal.

When the lines room parallel, the interior angles ~ above the exact same side of the transversal room supplementary. m∠1 + m∠2 = 180 m∠3 + m∠4 = 180


If two parallel currently are reduced by a transversal, the inner angles on the same side that the transversal are supplementary.
If 2 lines are reduced by a transversal and also the internal angles ~ above the very same side of the transversal are supplementary, the lines room parallel.

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In enhancement to the 4 pairs of called angles the are provided when working through parallel currently (listed above), over there are likewise some bag of "old friends" the are likewise working in parallel lines.

Vertical Angles: When directly lines intersect, vertical angles appear. vertical angles space ALWAYS equal in measure, even if it is the lines space parallel or not.

There space 4 sets of vertical angle in this diagram!

∠1 and also ∠2 ∠3 and also ∠4 ∠5 and ∠6 ∠7 and also ∠8

Remember: the lines require not it is in parallel to have vertical angle of same measure.


Linear Pair Angles: A linear pair room two nearby angles creating a directly line.

See more: Difference Between Formal Parameters And Actual Parameters, Formal And Actual Parameters

Angles forming a linear pair are ALWAYS supplementary.
due to the fact that a directly angle includes 180º, the two angles forming a straight pair likewise contain 180º once their procedures are added (making lock supplementary). m∠1 + m∠4 = 180 m∠1 + m∠3 = 180 m∠2 + m∠4 = 180 m∠2 + m∠3 = 180 m∠5 + m∠8 = 180 m∠5 + m∠7 = 180 m∠6 + m∠8 = 180 m∠6 + m∠7 = 180

Topical overview | Geometry summary | starrkingschool.net | MathBits" Teacher sources Terms that Use contact Person: Donna Roberts