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Finding Unknown Values in Vertical Angles

Finding Unknown Values in Vertical Angles
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2023-12-18 16:44
AngleGeometric ConstructionSlider Animation
This example demonstrates how to calculate missing values in vertical angles using geometric constructions. Key mathematical concepts include properties of vertical angles, angle measurement, and algebraic solving. Construction involves using GeoGebra commands like Element, Angle, and Textfield to create vertical angle diagrams, with dynamic adjustments via If and Polygon commands. Suitable for 6-8 grade students for geometry practice and classroom demonstrations.

GeoGebra Commands & Parameters

  1. Element(allCaseNum, Mod[countQuestion, Length[allCaseNum]] + 1) → caseNum
  2. Shuffle(Sequence[t, t, 20, angBig - 10, 2]) → allAngMini2, {20, 152, 22, 158, 86, 104, 38, 96, 140, 80, 44, 154, 162, 138, 130, 58, 26, 144, 46, 108, 52, 34, 122, 136, 102, 112, 150, 64, 72, 164, 148, 74, 132, 88, 54, 160, 76, 156, 62, 30, 126, 90, 84, 36, 94, 168, 128, 92, 98, 120, 78, 142, 134, 116, 100, 70, 42, 110, 60, 32, 40, 28, 146, 50, 82, 66, 166, 114, 106, 56, 48, 170, 124, 68, 24, 118}
  3. Shuffle(Sequence[t, t, 21, angBig - 12, 3]) → allAngMini3, {21, 39, 147, 165, 105, 102, 45, 126, 123, 93, 60, 150, 162, 129, 153, 48, 72, 30, 81, 96, 84, 90, 33, 51, 24, 57, 135, 99, 138, 111, 114, 144, 78, 36, 117, 108, 63, 156, 75, 69, 132, 87, 120, 141, 168, 42, 66, 27, 54, 159}
  4. Element(allAngMini2, Mod[countQuestion, Length[allAngMini2]] + 1) → angMini2
  5. Element(allAngMini3, Mod[countQuestion, Length[allAngMini3]] + 1) → angMini3
  6. Rotate(A, If[caseNum ≟ 1, angMini2°, angMini3°], O) → B
  7. Angle(A, O, B) → angAOB
  8. Textfield(input1) → InputBox1
  9. TextToUnicode(("" * InputBox1)) → studUniCurrent
  10. Rotate(A, angBig°, O) → AF
  11. Angle(B, O, AF) → angBOF
  12. If(caseNum ≟ 1, angMini2 / 2, angMini3 / 3) → ans1
  13. Angle(A, O, AF) → bigA
  14. Textfield(input2) → InputBox2
  15. Polygon(Zip[PixelsToPoint[Corner[1], Corner[3], Corner[5], A], A, {(pixelsLeft, pixelsTop), (pixelsLeft, y(Corner[5]) - pixelsBottom), Corner[5] - (pixelsRight, pixelsBottom), (x(Corner[5]) - pixelsRight, pixelsTop)}]) → borderBox
  16. Corner(5) → layoutAppSize
  17. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  18. Element({If[layoutX ≟ 16, layoutX - 5, 11], layoutX - 5}, layoutCase) → layoutHintSolnX
  19. Point(Vector[(1.8 * UnitVector[AngularBisector[AA, O, BB]])], 1) → posLabelAOB
  20. Point(Vector[(4.4 * UnitVector[AngularBisector[AA, O, AFF]])], 1) → posLabBig
  21. Segment(O, AF) → vert
  22. Segment(O, A) → hor
  23. Segment(O, B') → angSide
  24. Point(Vector[(1.8 * UnitVector[AngularBisector[B', O, AF]])], 1) → posLabelSol2
  25. Angle(A, O, B') → solCase1
  26. Point(Vector[(1.8 * UnitVector[AngularBisector[A, O, B']])], 1) → posLabelSol1
  27. Point(Vector[(2.2 * UnitVector[AngularBisector[BB, O, AFF]])], 1) → posLabelBOF
  28. Mirror(B, O) → BO
  29. Segment(O, BO) → angSide2
  30. Angle(AF, O, BO) → angVert
  31. If(showhint, 3, 0) → speed
  32. Rotate(A, If[caseNum ≟ 1, ((2 * aniSli) * input1°), ((3 * aniSli) * input1°)], O) → SA
  33. Segment(O, SA) → studSide
  34. Angle(A, O, SA) → studAng

AI Drawing Prompt Reference

Create a geometry diagram with a central vertex O and rays through points A and B. Draw a horizontal reference segment from O to A, and another ray from O passing through B. Mark and display the angle ∠AOB at O. Include a text input box for an unknown angle value (input1) and use it to define a rotated ray AF obtained by rotating A around O. Show angles involving AF such as ∠BOF and ∠AOF, and draw the segment from O to AF. Add the ray symmetric to B with respect to O to form a vertical-angle configuration, then mark the angle between AF and this symmetric ray, displaying the student answer area as a text field and keeping the diagram responsive to the entered value.
The prompt above was compiled from the original drawing commands and is for reference only.