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Angles and also Parallel Lines piersonforcongress.com Topical Summary | Geomeattempt Synopsis | MathBits" Teacher Resources Terms of Use Contact Person: Donna Roberts

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When a transversal intersects two or more lines in the exact same plane, a series of angles are developed. Certain pairs of angles are provided specific "names" based upon their locations in relation to the lines. These particular names might be provided whether the lines involved are parallel or not parallel.

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Alternating Interior Angles: The word "alternate" means "alternating sides" of the transversal.

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This name plainly explains the "location" of these angles. When the lines are parallel, the procedures are equal.
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∠1 and ∠2 are different internal angles ∠3 and also ∠4 are alternative interior angles

Alternating inner angles are "interior" (in between the parallel lines), and they "alternate" sides of the transversal. Notice that they are not adjacent angles (alongside one another sharing a vertex).

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


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If you draw a Z on the diagram, the different interior angles have the right to be found in the corners of the Z. The Z may additionally be backward:
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If two lines are reduced by a transversal and the different inner angles are congruent, the lines are parallel.
Alternative Exterior Angles: Words "alternate" suggests "alternating sides" of the transversal. The name plainly describes the "location" of these angles. When the lines are parallel, the steps are equal.

Alternating exterior angles are "exterior" (outside the parallel lines), and also they "alternate" sides of the transversal. Notice that, choose the different inner angles, these angles are not surrounding.

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


If 2 lines are cut by a transversal and also the alternative exterior angles are congruent, the lines are parallel.
Corresponding Angles: The name does not plainly explain the "location" of these angles. The angles are on the SAME SIDE of the transversal, one INTERIOR and also one EXTERIOR, yet not adjacent. The angles lie on the exact same side of the transversal in "corresponding" positions. When the lines are parallel, the actions are equal.
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∠1 and also ∠2 are corresponding angles ∠3 and also ∠4 are corresponding angles ∠5 and also ∠6 are corresponding angles ∠7 and ∠8 are corresponding angles

If you copy one of the equivalent angles and also you translate it alengthy the transversal, it will coincide through the various other matching angle. For instance, slide ∠ 1 down the transversal and also it will certainly coincide with ∠2.

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


If you attract a F on the diagram, the corresponding angles deserve to be uncovered in the corners of the F. The F may likewise be backward and/or upside-down:
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If 2 lines are cut by a transversal and the equivalent angles are congruent, the lines are parallel.
Interior Angles on the Same Side of the Transversal: The name is a summary of the "location" of the these angles. When the lines are parallel, the procedures are supplementary.
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∠1 and ∠2 are inner angles on the very same side of transversal ∠3 and ∠4 are interior angles on the same side of transversal

These angles are located exactly as their name describes. They are "interior" (between the parallel lines), and also they are on the same side of the transversal.

When the lines are parallel, the inner angles on the exact same side of the transversal are supplementary. m∠1 + m∠2 = 180 m∠3 + m∠4 = 180


If 2 parallel lines are reduced by a transversal, the interior angles on the exact same side of the transversal are supplementary.
If two lines are cut by a transversal and the interior angles on the exact same side of the transversal are supplementary, the lines are parallel.

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In enhancement to the 4 pairs of called angles that are supplied as soon as functioning with parallel lines (listed above), tbelow are likewise some pairs of "old friends" that are also working in parallel lines.

Vertical Angles: When right lines intersect, vertical angles show up. Vertical angles are ALWAYS equal in measure, whether the lines are parallel or not.

There are 4 sets of vertical angles in this diagram!

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

Remember: the lines need not be parallel to have vertical angles of equal measure.


Linear Pair Angles: A linear pair are 2 surrounding angles creating a straight line.

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Angles forming a straight pair are ALWAYS supplementary.
Due to the fact that a straight angle consists of 180º, the two angles creating a linear pair additionally contain 180º when their procedures are added (making them 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 Summary | Geometry Synopsis | piersonforcongress.com | MathBits" Teacher Resources Terms of Use Contact Person: Donna Roberts