"Equidistant" means the same distance (from the prefix "equi-", which means equal, and "distance"). Parallel lines are equidistant from each other. This means that every point on one line is always … [Read more...] about Parallel Lines are Equidistant
Lines and Angles
Lines and angles are two of the most basic elements of 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. A part of a line that is bounded by two points is called a line segment. 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:
The segment addition postulate states that if we have a line segment defined by two points, A and C, a third point , B, is on the same line if (and only if) the length of segment AB plus the length of segment BC is equal to the length of AC:
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°.
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
In today's lesson, we will show a simple method for proving the Consecutive Interior Angles Converse Theorem. The Consecutive Interior Angles Theorem states that the consecutive interior angles on … [Read more...] about Consecutive Interior Angles Converse Theorem
The three parallel lines theorem is another theorem that provides a ratio between line segments created by a transversal of parallel lines, similar to the Intercept Theorem. It states that if three … [Read more...] about Three Parallel Lines Theorem
In today's lesson, we will show how to prove the converse of the Angle Bisector Equidistant Theorem. The Angle Bisector Equidistant Theorem states that any point that is on the angle bisector is … [Read more...] about Converse of the Angle Bisector Equidistant Theorem
In today's lesson, we will prove the 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 … [Read more...] about Angle Bisector Equidistant 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
In today's lesson, we will show that two lines parallel to a third line are parallel to each other. In geometry, parallel lines are lines that do not meet. They do not intersect or touch each other … [Read more...] about Two Lines Parallel to a Third are Parallel to Each Other
In today's geometry lesson, we'll prove the converse of the Alternate Interior Angles Theorem. We have shown that when two parallel lines are intersected by a transversal line, the interior … [Read more...] about Converse Alternate Interior Angles 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
In today's lesson, we'll discuss the concepts of lines and angles in geometry, including line segments, line axioms, and how two intersecting lines form an angle. What is a line? A line is an … [Read more...] about Lines and Angles in Geometry