The blue line below is the graph of the equation y = 2x + 3 and the black line is y = 2x - 4. The converse is also true if two lines have the same slope, the two lines are parallel unless they overlap. In coordinate geometry, parallel lines have the same slope.
Alternate exterior angles are congruent.Alternate interior angles are congruent.Parallel lines cut by a transversal have the following properties: If two lines are parallel to the same line, they are parallel to each other.The slopes of two parallel lines are always equal.Parallel lines never intersect at any point along their lengths.Parallel lines are always equidistant from each other.How do you know if two lines are parallelīelow are some of the key properties of parallel lines that can be used to determine if two lines are parallel.
∠1, ∠3, ∠5, ∠7 are supplementary to ∠2, ∠4, ∠6, ∠8, respectively.Īlso, if any of the eight angles formed by two parallel lines and a transversal is a right angle, all the angles formed are right angles and the transversal is perpendicular to the two parallel lines. In summary, ∠1, ∠3, ∠5, ∠7 are congruent and ∠2, ∠4, ∠6, ∠8 are also congruent. Exterior angles on the same side of the transversal are supplementary, so ∠1 + ∠8 = 180° and ∠2 + ∠7 = 180°.Consecutive interior angles are supplementary, so ∠3 + ∠6 = 180° and ∠4 + ∠5 = 180°.Corresponding angles on the same side of the transversal are congruent, so ∠1≅∠5, ∠2≅∠6, ∠3≅∠7, and ∠4≅∠8.Alternate interior angles are congruent, so ∠3≅∠5 and ∠4≅∠6.Alternate exterior angles are congruent, so ∠1≅∠7 and ∠2≅∠8.Several relationships exist among these angles. Vertical angles - pairs of congruent angles formed by the intersection of two straight lines.∠3 & ∠6, ∠4 & ∠5 are pairs of consecutive interior angles. Consecutive interior angles - angles formed on the inside of the transversal that are supplementary also referred to as co-interior angles.∠1, ∠2, ∠7, ∠8 are alternate exterior angles. Alternate exterior angles - angles formed on the outside of two parallel lines cut by a transversal.∠3, ∠4, ∠5, ∠6 are alternate interior angles. Alternate interior angles - angles formed on the inside of two parallel lines cut by a transversal.Supplementary angles - either of 2 angles whose sum is 180°.Corresponding angles - angles that occupy the same relative position when a transversal cuts 2 parallel lines.The following terms are used to refer to the angle pairs formed by a transversal and a pair of parallel lines. When 2 lines are cut (intersected) by a third line, called a transversal, 8 angles are formed. You can also place arrows on the lines, as in the figure above, to show that they are parallel. The symbol to show parallel lines is "//". For the railroad tracks to work properly and allow a train to move across them, they cannot ever intersect. Some real life examples of parallel lines are railroad tracks. Parallel lines are coplanar lines that are equidistant from each other throughout their entire lengths. Line segments and rays that are parts of parallel lines are also parallel. Parallel lines are lines in the same plane that do not intersect. Home / geometry / line / parallel lines Parallel lines
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