Midpoints, Lines and Planes

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A series of free, online High School Geometry Video Lessons and solutions.
Examples, solutions, videos, worksheets, and activities to help Geometry students.

In this lesson, we will learn

  • midpoints and congruent segments
  • finding the midpoint using the midpoint formula
  • parallel planes and lines
  • vertex and diagonals

You can also practice using the midpoint formula worksheet.

The following diagram shows how to use the midpoints formula to find the midpoint for the two points (x1,y1) and (x2,y2). Scroll down the page for more examples and solutions on how to use the midpoint formula.

Midpoint Formula

Midpoints and Congruent Segments

When learning about midpoints, it is also important to understand the concept of congruent segments. Congruent line segments are line segments with the same length. In a line segment, there is one point that will bisect the line segment into two congruent line segments. This point is called the midpoint.
How to identify, define and label a midpoint?

Finding the Midpoint

By using x and y coordinates, it is easy to find the midpoint of a line segment. Finding the midpoint is calculated by taking the average of the x coordinates and then taking the average of the y coordinates. For example, if we had two coordinates located at (1,3) and (5, 7) our midpoint would be (3, 5).
How to find the midpoint of a segment with endpoints in rectangular coordinates?
How to write the midpoint formula?
The Midpoint Formula - Finding the Midpoint

Parallel Planes and Lines

In Geometry, a plane is any flat, two-dimensional surface. Two planes that do not intersect are said to be parallel. Parallel planes are found in shapes like cubes, which actually has three sets of parallel planes. The two planes on opposite sides of a cube are parallel to one another.
How to identify parallel lines, a line parallel to a plane, and two parallel planes?
Parallel and Perpendicular Lines and Planes

Vertices, diagonals, and sides

The plural forms of vertex, vertices are typically intersections or corners in figures. In an angle, the vertex is where two lines, rays, or segments meet. A diagonal is a line segment whose endpoints are vertices. In a polygon, a vertex is where two edges or sides meet. In a polyhedron, a vertex is where three edges meet.
How the vocabulary word vertex applies to different objects in Geometry?

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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