Big Ideas Geometry Chapter 3

Parallel Lines

Parallel Lines

lines in the same plane that do not intersect
always have the same slope and a different y-intercept

Perpendicular Lines

lines whose intersections is a 90 degree angle
the product of their slopes is always -1

Skew Lines

lines in different planes that do not intersect and are not parallel

Transversal Lines

a line that intersect two or more coplanar lines at different points

Corresponding Angles

when angles have corresponding positions

Alternate Interior Angles

when angles lie between the two lines and on opposite sides of the transversal

Alternate Exterior Angles

when angles lie outside the two lines and on opposite sides of the transversal

Same Side Interior Angles

when angles lie between the two lines and on the same side of the transversal (interior)

Same Side Exterior Angles

when angles lie between the two lines and on the same side of the transversal

Corresponding Angles Postulate

If parallel lines are cut by a transversal, then the corresponding angles are congruent.

Alternate Interior Angles Theorem

If parallel lines are cut by a transversal, then the alternate interior angles are congruent,

Alternate Exterior Angles Theorem

If parallel lines are cut by a transversal, then the alternate exterior angles are congruent.

Same Side Interior Angles Theorem

If parallel lines are cut by a transversal, then the same side interior angles are supplementary.

Converse of Corresponding Angles Postulate

If two coplanar lines are cut by a transversal and the corresponding angles are congruent, then the lines are parallel.

Converse of Alternate Interior Angles Theorem

If two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.

Converse of Alternate Exterior Angles Theorem

If two lines are cut by a transversal and the alternate exterior angles are congruent, then the lines are parallel.

Converse of Same Side Interior Angles Theorem

If two lines are cut by a transversal and the same side interior angles are supplementary, then the liens are parallel.

slope formula

change in y's
---------------
change is x's

slope of vertical lines

no slope

slope of horizontal lines

m=0

Parallel Lines Theorem

In a coordinate plane, two non vertical lines are parallel if and only if they have the same slope.

Perpendicular Lines Theorem

In a coordinate plane, two non vertical lines are perpendicular if and only if the product of their slopes is -1.

Linear Pair Perpendicular Theorem

If two lines intersect to form a congruent linear pair, the lines are perpendicular.

Perpendicular Transversal Theorem

If a transversal is perpendicular to one of two parallel lines then it is parallel to the other line.

Lines Parallel to a Transversal Theorem

If two lines are perpendicular to the same line, then the lines are parallel.

Point-slope formula

y-y=m(x-x)

Standard Form

Ax+By=C

Slope Intercept Form

y=mx+b