Example 5.  Constructing a right isosceles triangle (with an introduction to the Measure menu).

We now construct an isosceles right triangle.  An isosceles triangle has at least two congruent sides.  Since we already know how to construct an equilateral triangle (which is an isosceles triangle since it has three congruent sides), we will construct a triangle with two congruent sides and a right angle between the congruent sides. This will force the triangle to have exactly two congruent sides.

Open a new sketch and construct segment AB.  Construct the perpendicular line to AB through B.  Now we need to construct vertex C on the perpendicular line such that segment BC is congruent to segment AB.  Remember that we used the COMPASS TOOL to construct congruent segments.  In Example 3, Constructing an Equilateral Triangle, we constructed circles using two points (one serving as the center and the other as the endpoint of the radius).  We present an alternative (but very close) way to construct a circle.  Use the SELECTION ARROW TOOL to select vertex B (the center) and segment AB (the radius) only.  Open the Construct menu and select the Circle By Center + Radius command.  See Figure 14.

Figure 14

Read the caption on the bottom left corner of the sketch (in version 4 only).  The circle appears selected (thick line).  Also select the perpendicular line.  Open the Construct menu and select the Intersections command. We only need one of the points so label either one as point C. Select the other intersection point, the perpendicular line and the circle.  Use the Hide Objects command (Display menu) to hide them.  See Figure 15.

Construct segments BC and AC.

Figure 15

Before performing the drag test, we will measure segments BC and AC to observe their changes when we drag the triangle.  Select segments BC and AC only.  Open the Measure menu and select the Length command.  See Figure 16.  Two measurements (with labels in version 4) should appear on the screen.  (In version 3 you need to label the endpoints so you know which measurement corresponds to what segment.)

Figure 16

Now perform the drag test by dragging any vertex.  Observe how the lengths of the segments remain the same indicating that the segments are congruent.  This confirms that the triangle is an isosceles right triangle.