The Angle Bisector Equidistant Theorem states that any point that is on the angle bisector is an equal distance ("equidistant") from the two sides of the angle.The converse of this is also true. … [Read more...] about Converse of the Angle Bisector Equidistant Theorem

# Lines and Angles

## What is a line?

A line is an abstract concept. It has no width, only length, and that length is infinite in both directions. One of the formal definitions of a line is that it is the collection of all points that are the same distance from two other points on a plane:

## Angles

When 2 lines or line segments intersect, they form angles:

We measure angles in units called degrees, and marked with a °, where a full circle is 360°.

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*Now that we've briefly explained the basic concept of lines and angles in geometry, let's scroll down to the post below that explains these concepts more in depth. For specific geometry problems in the area of lines and angles, check out the following links: Intersecting Lines and Angles Parallel Lines Perpendicular Lines *

## Angle Bisector Equidistant Theorem

When two rays intersect at a point, they create an angle, and the rays form the two sides of this angle. A line that splits this angle into two equal angles is called the angle bisector.The Angle … [Read more...] about Angle Bisector Equidistant Theorem

## Intercept Theorem

The Intercept theorem provides the ratios between the line segments created when two parallel lines are intercepted by two intersecting lines. It is sometimes called "Thales' Theorem" (not to be … [Read more...] about Intercept Theorem

## Two Lines that are Parallel to a Third Line are Parallel to Each Other

One way to show that two lines are parallel to each other is to find two corresponding angles created by a transversal line that are congruent, as we have proven here.We can use this theorem to … [Read more...] about Two Lines that are Parallel to a Third Line are Parallel to Each Other

## Converse Alternate Interior Angles Theorem

We have shown that when two parallel lines are intersected by a transversal line, the interior alternating angles and exterior alternating angles are congruent (that is, they have the same measure of … [Read more...] about Converse Alternate Interior Angles Theorem

## Shortest Distance Theorem

The shortest distance theorem states that the shortest distance between a point P, and a line, l, is the perpendicular line from P to l. It is also called the "perpendicular distance."It is … [Read more...] about Shortest Distance Theorem

## Lines and Angles in Geometry

What is a line?A line is an abstract concept. It has no width, only length, and that length is infinite in both directions. One of the formal definitions of a line is that it is the collection of … [Read more...] about Lines and Angles in Geometry

## Linear Pair Perpendicular Theorem

Prove:If two straight lines intersect at a point and form a linear pair of equal angles, they are perpendicular.Given:m∠1 = m∠2, prove that the lines L1 and … [Read more...] about Linear Pair Perpendicular Theorem

## Converse of the Corresponding Angles Theorem

We had earlier said axiomatically, with no proof, that if two lines are parallel, the corresponding angles created by a transversal line are congruent. Now let’s prove an important converse theorem: … [Read more...] about Converse of the Corresponding Angles Theorem

## Alternate Interior Angles Theorem

Prove:Interior alternating angles and exterior alternating angles are congruent (that is, they have the same measure of the angle.)How to approach this problem?So how do we go about … [Read more...] about Alternate Interior Angles Theorem