Angles and Parallel Lines altoalsimce.org Topical synopsis | Geometry outline | MathBits" Teacher sources Terms that Use call Person: Donna Roberts
as soon as a transversal intersects 2 or much more lines in the very same plane, a collection of angles room formed. Particular pairs the angles space given particular "names" based ~ above their areas in relation to the lines. These particular names may be supplied whether the lines connected are parallel or no parallel.
Alternate inner Angles: The indigenous "alternate" means "alternating sides" of the transversal.
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This name plainly describes the "location" of this angles. As soon as the lines space parallel, the measures are equal.
∠1 and ∠2 are alternative interior angles ∠3 and also ∠4 are alternative interior angles
alternative interior angles are "interior" (between the parallel lines), and also they "alternate" sides of the transversal. Notice that they room not adjacent angles (next come one an additional sharing a vertex).
When the lines space parallel, the alternate interior anglesare same in measure. m∠1 = m∠2 and also m∠3 = m∠4
If you draw a Z top top the diagram, the alternate interior angles have the right to be uncovered in the corners of the Z. The Z may also be backward:
If 2 lines are reduced by a transversal and the alternate interior angles room congruent, the lines room parallel.
Alternate Exterior Angles: The word "alternate" means "alternating sides" the the transversal. The name plainly describes the "location" of these angles. Once the lines are parallel, the procedures are equal.
alternative exterior angles space "exterior" (outside the parallel lines), and also they "alternate" sides of the transversal. Notice that, choose the alternating interior angles, this angles space not adjacent.
When the lines space parallel, the alternating exterior angles room equal in measure. m∠1 = m∠2 and also m∠3 = m∠4
If 2 lines are cut by a transversal and the alternate exterior angles room congruent, the lines room parallel.
Corresponding Angles: The name does not plainly describe the "location" of this angles. The angles are on the same SIDE of the transversal, one INTERIOR and also one EXTERIOR, however not adjacent. The angle lie on the very same side of the transversal in "corresponding" positions. when the lines room parallel, the actions are equal.
∠1 and also ∠2 are corresponding angles ∠3 and ∠4 are corresponding angles ∠5 and also ∠6 are matching angles ∠7 and also ∠8 are corresponding angles
If you copy among the matching angles and you interpret it follow me the transversal, it will certainly coincide v the other matching angle. Because that example, on slide ∠ 1 under the transversal and also it will certainly coincide through ∠2.
When the lines room parallel, the equivalent angles room equal in measure. m∠1 = m∠2 and m∠3 = m∠4 m∠5 = m∠6 and also m∠7 = m∠8
If you attract a F ~ above the diagram, the matching angles can be found in the corners that the F. The F may likewise be backward and/or upside-down:
If 2 lines are cut by a transversal and also the equivalent angles are congruent, the lines room parallel.
Interior angles on the exact same Side that the Transversal: The name is a summary of the "location" the the this angles. once the lines space parallel, the procedures are supplementary.
∠1 and also ∠2 are internal angles top top the same side that transversal ∠3 and also ∠4 are interior angles top top the very same side that transversal
this angles room located specifically as their surname describes. They space "interior" (between the parallel lines), and they space on the same next of the transversal.
When the lines room parallel, the internal angles ~ above the same side of the transversal space supplementary. m∠1 + m∠2 = 180 m∠3 + m∠4 = 180
If 2 parallel currently are cut by a transversal, the internal angles ~ above the exact same side that the transversal room supplementary.
If 2 lines are reduced by a transversal and the internal angles top top the exact same side the the transversal space supplementary, the lines are parallel.
Vertical Angles: When right lines intersect, vertical angles appear. upright angles room ALWAYS equal in measure, whether the lines room parallel or not.
There space 4 to adjust of vertical angle in this diagram!
∠1 and ∠2 ∠3 and also ∠4 ∠5 and ∠6 ∠7 and ∠8
Remember: the lines need not it is in parallel to have vertical angle of same measure.
Linear Pair Angles: A direct pair are two adjacent angles developing a directly line.
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Angles creating a linear pair room ALWAYS supplementary.
because a right angle contains 180º, the two angles developing a direct pair additionally contain 180º as soon as their actions are included (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