Introduction of Dynamic Geometry

　

There are different dynamic geometry software, including “Sketchpad”, “Cabri”, “Dr. Geo” and “Geometry Expert”. They have many common features. The following examples can be used in Sketchpad (but they can also be used in other dynamic geometry software with only very few modifications.) You may try also the exercises in order to get familiar with the software. (Please note that the exercises are for teachers only; they may be too difficult to students.)

　

Example 1 (Perpendicular bisectors of a triangle) [Link to the JAVA Sketch]

1.

Construct lines AB, BC and CA to form a triangle.

2.

Select AB and choose “Construct”, “Point at midpoint” to construct the midpoint D of AB. Similarly construct the midpoint E of BC.

3.

Select both AB and E by using the SHIFT key. Then choose “Construct”, “Perpendicular line” to construct the perpendicular bisector of AB. Similarly, construct the perpendicular bisector of BC.

4.

Construct the intersection point F of the two perpendicular bisectors.

5.

Select the point F and then choose “Display”, “Trace”.

6.

Drag B to observe the locus of F. Make your conjecture.

　

Vary A and C and repeat Step 6.

　

Example 2 (Mid-points of a quadrilateral) [Link to the JAVA Sketch]

1.

Construct lines AB, BC, CD and DA to form a quadrilateral.

2.

Select AB and choose “Construct”, “Point at midpoint” to construct the midpoint E of AB. Similarly construct the midpoints F, G and H of BC, CD and DA respectively.

3.

Construct lines EF, FG, GH and HF to form a quadrilateral.

4.

Vary A, B, C and D to observe the change of EFGH. Make your conjecture.

5.

Construct line AC and discuss the proof of your conjecture.

　

Exercises of Dynamic Geometry Constructions (Sketchpad or Cabri)

　

  1. Constructing a Rhombus
    2.

    　

    1.

    Construct a segment AB .

    　

    2.

    Construct a circle AB.

    　

    3.

    Construct a segment AC, where C is any point on the circle.

    　

    4.

    Construct a line through C, parallel to AB.

    　

    5.

    Construct a line through B, parallel to AC.

    　

    6.

    Construct the intersection, D, of the lines through B and C.

    　

    7.

    Hide the circle and lines.

    　

    8.

    Construct the segments CD and BD.

    　

  2. The Centroid of a Triangle
    3.

    　

    1.

    Construct the triangle ABC.

    　

    2.

    Construct the mid-points on each side.

    　

    3.

    Construct two medians, AD and BF, and their intersection point G.

    　

    4.

    Construct the third median.

    　

    5.

    Measure the distances from B to G and from F to G.

    　

    6.

    Calculate BG/FG.

    　

    7.

    Construct interiors of the small triangles like AFG, and measure their areas.

    　

  3. Radian Measure
    4.

    　

    1.

    Construct a segment AB and the circle AB.

    　

    2.

    Construct a point on the circle.

    　

    3.

    Select A, B and C, and construct an arc BC [Construct Arc on Circle].

    　

    4.

    Measure the length of the arc BC, radius of the circle and calculate their ratio.

    　

    5.

    You may also construct the sector ABC to highlight the arc. [Construct Sector Interior after selecting the arc].

    　

    　

  4. A Sine Wave Tracer
    5.

    　

    1.

    Construct a segment AB and a point C.

    　

    2.

    Construct a circle with centre A and radius endpoint C.

    　

    3.

    Construct a point D on AB and a line perpendicular to AB through D.

    　

    4.

    Construct a segment AE, with E on the circle.

    　

    5.

    Construct a line parallel to AB, through E.

    　

    6.

    Construct the point of intersection, F. If you consider your circle to be a unit circle, the height of the point F above AB is the value of the sine of angle A.

    　

    7.

    Move the point D so that it is just to the right of the circle.

    　

    8.

    Select the point F and choose Trace Point in the Display menu.

    　

    9.

    Select, in order, D, AB, E and the circle.

    　

    10.

    Make an action button [Edit Action button Animation] that animate points D on AB, one-way, and animates point E on the circle, one-way.

　

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