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Area of Two Triangles on the Same Base and Between the Same Parallels

Area of Two Triangles on the Same Base and Between the Same Parallels
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2020-10-22 14:56
TriangleCoordinate GeometryGeometric Construction
In collections CLASS IX CBSE MATHS ACTIVITIES
This example demonstrates two triangles on the same base and between the same parallels, proving their equal areas through dynamic visualization. Key math concepts include triangle area formulas, properties of parallel lines, and geometric proofs. Construction highlights the use of GeoGebra commands like Intersect, Point, Polygon, and PointIn. Suitable for high school mathematics education to intuitively understand the properties of equal-area triangles between parallel lines.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → C
  3. Polygon(A, B, C) → t1, c, a, b
  4. PointIn(t1) → Pointt1
  5. Polygon(A, D, C) → t2, c_1, a_1, d
  6. PointIn(t2) → Pointt2

AI Drawing Prompt Reference

On a coordinate plane, place one vertex at the origin and two other vertices on the x-axis, forming a shared base. Construct two triangles that share this same base, with their third vertices located on opposite sides of the base but between two parallel lines. Draw the first triangle and mark a point inside it, then draw the second triangle and mark a point inside it. Ensure both triangles have equal base length and equal height (since the vertices lie between the parallels), visually demonstrating their equal areas.
The prompt above was compiled from the original drawing commands and is for reference only.