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Mathematics Dictionary
Dr. K. G. Shih
Construction Methods
Subjects


  • GE 11 00 | - Outlines
  • GE 11 01 | - Bisect an anglr
  • GE 11 02 | - Bisect a line
  • GE 11 03 | - Construct triangle by three given lines
  • GE 11 04 | - Construct triangle by three given heights of triangle
  • GE 11 05 | - Construct triangle by three given medians of triangle
  • GE 11 06 | - Draw a circle passing three given points
  • GE 11 07 | - Draw a circle with 3 sides of triangle as tangent (1)
  • GE 11 08 | - Draw a circle with 3 sides of triangle as tangent (1)
  • GE 11 09 | - Construct centroid of triangle
  • GE 11 10 | - Construct ortho-center of triangle
  • GE 11 11 | - Change quadrilateral to an equal area triangle
  • GE 11 12 | - Draw an ex-central triangle
  • GE 11 13 | - Draw tangent to a circle
  • GE 11 14 | - Draw parabola using locus definition
  • GE 11 15 | - Draw ellipse using locus definition
  • GE 11 16 | - Construct a pedal triangle
  • GE 11 17 | - Give 2 angles and one height to draw a triangle
  • GE 11 18 | - New
    • Answers


    GE 11 01. Bisect an angle

    Question
    • Give an angle, how to bisect the angle ?
    Reference
    Go to Begin

    GE 11 02. Bisect a line

    Question
    • Give a line, how to bisect the line ?
    Reference
    Go to Begin

    GE 11 03. Construct triangle by three given lines

    Question
    • Three lines are givne
    • Construct a triangle
    Reference
    Go to Begin

    GE 11 04. Construct triangle by three given heights of triangle

    Question
    • Three heights of triangle are givne
    • Construct a triangle
    Reference
    Go to Begin

    GE 11 05. Construct triangle by three given medians of triangle

    Question
    • Three medians of triangle are givne
    • Construct a triangle
    Reference
    Go to Begin

    GE 11 06. Draw a circle passing three given points

    Question
    • Give three points
    • Draw a circle passing the given points
    Reference     Hint
    • The center of circle is called circum-center
    • The circle is called circum-circle

    Go to Begin

    GE 11 07. Draw a circle and the sides of triangle are tangents

    Question
    • Give a triangle
    • Draw a circle and the sides of triangle are tangents of the circle
    Reference     Hint
    • The center of the circle is called in-center of triangle
    • The circle is called in-circle

    Go to Begin

    GE 11 08.Draw a circle and the sides of triangle are tangents

    Question
    • Give a triangle
    • Draw a circle and the one side of triangle is tangent of the circle
    • The produced of other two sides of triangle are also tangenst of the circle
    Reference     Hint
    • The center of the circle is called ex-center of triangle
    • The circle is called ex-circle

    Go to Begin

    GE 11 09. Construct centroid of triangle

    Reference
    Go to Begin

    GE 11 10. Construct ortho-center of triangle
    Reference
    Go to Begin

    GE 11 11. Change quadrilateral to an equal are triangle

    Reference
    Go to Begin

    GE 11 12. Construct an ex-central triangle

    Reference
    Go to Begin

    GE 11 13. Draw tangent to circle

    Reference
    Go to Begin

    GE 11 14. Draw parabola using locus definition

    Locus of parabola
    • Moving point to fixed point and fixed line has same distance
    • Fixed point is focus and fixed line is directrix
    Construction
    • Draw a fixed point F
    • Draw a fixed line AB. F to line AB is D
    • Draw a line 1 perpendicular to line AB at Q
      • Join Q and F
      • Bisect line QF and bisector meet line 1 at P1
      • P1 is a point on parabola
    • Draw a line 2 perpendicular to line AB at R
      • Join R and F
      • Bisect line RF and bisector meet line 2 at P2
      • P2 is a point on parabola
    • Draw a line 3 perpendicular to line AB at S
      • Join S and F
      • Bisect line SF and bisector meet line 3 at P3
      • P3 is a point on parabola
    • Draw more points on parabola
    • Draw the vertex of the paraboa which is between F and directrix
    • Join all the points smoothly which will be the required parabola
    Reference
    • Study subjects : Program 02 03
    • Method
      • Click Menu
      • Click section 3 in upper box
      • Click program 5 in lower box
      • Click Re-plot to see next diagram

    Go to Begin

    GE 11 15. Draw ellipse using locus definition

    Locus of parabola
    • Moving point P to two fixed points keeps PF + PG = 2*a
    • Two fixed points are foci and a is the major semi-axis
    Construction
    • Draw two fixed points G and F
    • Draw a center point between G and F. Assume the center is (0,0)
    • Draw a line 1 starting at G to point Q
      • Join Q and F
      • Bisect line QF and bisector meet line 1 at P1
      • P1 is a point on ellipse
    • Draw a line 2 starting at G to point R
      • Join R and F
      • Bisect line RF and bisector meet line 2 at P2
      • P2 is a point on ellipse
    • Draw a line 3 starting at G to point S
      • Join S and F
      • Bisect line SF and bisector meet line 3 at P3
      • P3 is a point on ellipse
    • Draw more points on ellipse as above
    • Draw the vertices of the ellipe which are (-a,0) and (a,0) on the ellipse
    • Join all the points smoothly which will be the required ellipse
    Reference
    • Diagram : Program 03 05
    • Method
      • Click Menu
      • Click section 3 in upper box
      • Click program 5 in lower box
      • Click Re-plot to see next diagram

    Go to Begin

    GE 11 16. Construct a pedal triangle

    Reference
    Go to Begin

    GE 11 17. Give 2 angles and one height to draw a triangle

    Draw a triangle using the given angles
    • Let the triangle be UVW
    • Let the given height h be perpendicular to UV which is parallel to AB
    Draw triangle ABC with given height perpendicular to AB
    • Draw a line AP parallel to UV
    • At point A draw line AQ parallel to UW
    • Draw a line RS parallel to AP which have distance h from AP
    • Line RS and line AQ meet at C
    • At point C draw a line parallel to VW and meet line AP at B
    • ABC is the required triangle
    Proof
    • Since triangle UVW is similar to triangle ABC
    • Hence angles of triangle ABC are equal the given angles
    • The height from C to AB is h which is the given height
    • Triangle ABC is required triangle

    Go to Begin

    GE 11 18. Construct a pedal triangle

    Reference
    Go to Begin

    GE 11 00. Outline

    • 01. Bisect an angle
    • 02. Bisect a line
    • 03. Construct a triangle using 3 given lines
    • 04. Construct a triangle using 3 given heights of triangle
    • 05. Construct a triangle using 3 given medians of triangle
    • 06. Construct a circum-center of triangle
    • 07. Construct a in-center of triangle
    • 08. Construct a ex-center of triangle
    • 09. Construct a centroid of triangle
    • 10. Construct a ortho-center of triangle

    Go to Begin
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