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45-45-90 Triangle: Quick Investigation

45-45-90 Triangle: Quick Investigation
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2019-06-26 09:39
TriangleCircleAngleGeometric ConstructionSlider Animation
This example demonstrates the properties and construction of an isosceles right triangle. It involves core concepts like isosceles triangles, right triangles, angles, and geometric mean. The construction utilizes GeoGebra commands such as Sequence, Segment, Circle, OrthogonalLine, Intersect, Dilate, Rotate, Angle, and Polygon. Suitable for middle school and above, this activity is ideal for geometric exploration and concept understanding.

GeoGebra Commands & Parameters

  1. Sequence(Rotate[(1, 0), i°, (0, 0)], i, 15, 360, 15) → list1
  2. Segment(B, A) → g
  3. Circle(B, A) → h
  4. OrthogonalLine(B, g) → i
  5. Intersect(h, i) → I, J
  6. Dilate(B, If[0 < j ≤ 1, 1 - j, 0], A) → G'
  7. Segment(B, G') → k
  8. Rotate(B, If[1 < j ≤ 2, ((j - 1) * π / 2), π / 2], B) → G'_1
  9. Rotate(G', If[1 < j ≤ 2, ((j - 1) * π / 2), π / 2], B) → C
  10. Segment(G'_1, C) → k'
  11. Angle(A, B, C) → α
  12. Dilate(J, If[2 < j ≤ 3, 3 - j, 0], A) → J'
  13. Segment(J, J') → l
  14. Polygon(B, A, J) → poly2, j_1, g_1, h_1

AI Drawing Prompt Reference

Draw an isosceles right triangle to demonstrate its properties and construction. Start by drawing a circle and a line segment, then find their intersection points. Next, scale one intersection point to the center of the circle and connect them. Rotate the line segment to form a 45-degree angle, and connect the rotated segment to the scaled point. Finally, scale the other intersection point to the center and connect them to complete the isosceles right triangle.
The prompt above was compiled from the original drawing commands and is for reference only.