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Determining if a Triangle is Right

Determining if a Triangle is Right
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2015-02-21 00:43
TriangleTrigonometryGeometric Construction
In collections PARCC Math III Unit 5 Lesson 7
This example demonstrates how to determine if a given triangle is a right triangle using side lengths. Key math concepts include the Pythagorean theorem, triangle classification, and distance formulas. GeoGebra commands used are Segment, Angle, Textfield, FractionText, and If for construction and analysis. Suitable for high school mathematics students and teachers for instructional purposes.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a
  2. Segment(A, C) → b
  3. Segment(B, C) → c
  4. Angle(A, B, C) → α
  5. Angle(B, A, C) → β
  6. Angle(A, C, B) → γ
  7. Textfield(A) → inputBox1
  8. Textfield(B) → inputBox2
  9. Textfield(C) → inputBox3
  10. Segment(A_1, B_1) → a_1
  11. Textfield(A_1) → inputBox1_1
  12. Textfield(B_1) → inputBox2_1
  13. FractionText(abs((y(C) - y(B)) / (x(C) - x(B)))) → BC
  14. FractionText(abs((y(C) - y(A)) / (x(C) - x(A)))) → AC
  15. FractionText(abs((y(B) - y(A)) / (x(B) - x(A)))) → AB
  16. Segment(B_2, C_1) → c_1
  17. Textfield(B_2) → inputBox2_2
  18. Textfield(C_1) → inputBox3_1
  19. If(numAC < 0, "-", "") → AC2
  20. FractionText((y(C_1) - y(B_2)) / (x(C_1) - x(B_2))) → BC_1
  21. If(numAB < 0, "-", "") → AB2
  22. If(numBC < 0, "-", "") → BC2
  23. If(pA ≟ -1, "AB perpendicular to AC", If[pB ≟ -1, "AB perpendicular to BC", If[pC ≟ -1, "AC perpendicular to BC", "None Perpendicular"]]) → answer