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Median Divides Triangle Area

Median Divides Triangle Area
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2015-01-02 01:53
TrianglePolygonGeometric Construction
This example demonstrates constructing a parallelogram using medians and proves that areas on the same base and same height are equal. Key concepts include medians and properties of parallelograms. It uses Midpoint, Polygon, Line, Circle, Intersect commands in GeoGebra. Suitable for middle school and above students learning geometric construction.

GeoGebra Commands & Parameters

  1. Midpoint(A, C) → E
  2. Polygon(E, C, B) → poly2, b_1, e_1, c
  3. Midpoint(B, A) → D
  4. Midpoint(C, B) → F
  5. Polygon(A, E, B) → poly1, b, a, e
  6. Line(A, c) → g
  7. Line(C, c) → h
  8. Circle(E, C) → d
  9. Line(B, b_1) → i
  10. Intersect(g, i) → G
  11. Polygon(A, B, G) → poly3, g_1, a_1, b_2

AI Drawing Prompt Reference

Draw a triangle ABC, find the midpoints E and F of sides AC and BC respectively, and draw two parallelograms with E and F as one vertex and B and C as the other vertex. Then, find the midpoint D of side AB, and draw another parallelogram with D as one vertex and A and B as the other vertex. Next, draw a line g from A to C, a line h from C to C, a circle d with E and C as the center and radius, and a line i from B to B. Find the intersection point G of lines g and i, and draw the last parallelogram with A, B, and G as vertices.
The prompt above was compiled from the original drawing commands and is for reference only.