Trapezoid median (midline, midsegment) definition (original) (raw)
A line segment between the midpoints of the legs of a trapezoid
Also known as midline or midsegment
Try this Drag the orange dots on each vertexto reshape the trapezoid. Notice the behavior of the red median line.
Properties
The median line is always parallel to the bases. Adjust the trapezoid above by dragging any vertex and convince yourself this is so.
The length of the median is the average length of the bases, or using the formula:
If one of the bases is zero length, the result is a triangle. and is identical to the triangle midsegment case. The median line will then be half the remaining base. Try this out in the figure above by moving A to overlap B.
The median line is halfway between the bases. Adjust the trapezoid above by dragging any vertex and convince yourself this is so.
The median divides the trapezoid into two smaller trapezoids each with half the altitude of the original.
The area of a trapezoid is the altitude × median. See Area of a trapezoid
Things to try
- In the figure above, click 'hide details'.
- Adjust the points A,B,C,D to create a new trapezoid.
- Calculate the length of the median
- Click 'show details' to check your answer.
Other polygon topics
General
- Polygon general definition
- Quadrilateral
- Regular polygon
- Irregular polygon
- Convex polygons
- Concave polygons
- Polygon diagonals
- Polygon triangles
- Apothem of a regular polygon
- Polygon center
- Radius of a regular polygon
- Incircle of a regular polygon
- Incenter of a regular polygon
- Circumcircle of a polygon
- Parallelogram inscribed in a quadrilateral
Types of polygon
- Square
- Diagonals of a square
- Rectangle
- Diagonals of a rectangle
- Golden rectangle
- Parallelogram
- Rhombus
- Trapezoid
- Trapezoid median
- Kite
- Inscribed (cyclic) quadrilateral
Area of various polygon types
- Regular polygon area
- Irregular polygon area
- Rhombus area
- Kite area
- Rectangle area
- Area of a square
- Trapezoid area
- Parallelogram area
Perimeter of various polygon types
- Perimeter of a polygon (regular and irregular)
- Perimeter of a triangle
- Perimeter of a rectangle
- Perimeter of a square
- Perimeter of a parallelogram
- Perimeter of a rhombus
- Perimeter of a trapezoid
- Perimeter of a kite
Angles associated with polygons
- Exterior angles of a polygon
- Interior angles of a polygon
- Relationship of interior/exterior angles
- Polygon central angle
Named polygons
- Tetragon, 4 sides
- Pentagon, 5 sides
- Hexagon, 6 sides
- Heptagon, 7 sides
- Octagon, 8 sides
- Nonagon Enneagon, 9 sides
- Decagon, 10 sides
- Undecagon, 11 sides
- Dodecagon, 12 sides
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