The most important thing of isosceles triangle is the unity of three lines, which can be easily understood by means of dynamic demonstration of geometric sketchpad. The steps of making isosceles triangle three-in-one courseware with geometric sketchpad are as follows:

1. Height of the construction triangle

Select the linear ruler tool to construct an acute triangle ABC；; Select point B and line segment AC, and click to construct a vertical line, so that the vertical line segment AC is at point D; Select point B and point D, and click Construct | Line Segment to make line segment BD and vertical line become dotted line; Select the marking tool to mark ∠ BDC at right angles; Pulling point B makes ∠A become obtuse, but the vertical foot disappears; Select point A and point C, click to construct a straight line, and make a straight line AC perpendicular to point E; Select the marking tool and mark ∠BEC as a right angle. At this point, drag point B to find the virtual and real vertical line.

2. Construct the triangle midline

Select the line segment AC, click the construction midpoint |, and make the midpoint f of the line segment AC to construct the line segment BF; Right-click the line segment BF and select red in the color bar of the pop-up dialog box to get the red line segment BF.

3. Draw the bisector of the triangle angle

Select points A, B and C in turn, click on the bisector of angle | to get the bisector of ∠B, change its color to purple, and point out the intersection point G between the bisector and AC with the mouse; Select the marking tool and mark ABG and CBG.

Measure angle and length

Select points A, B and G in turn (or directly select the corner marker), click Measure | Angle to measure the degree of ∠ABG; Similarly, measure the angle of ∠CBG; Select point B and point A, click Measure | Distance to measure the length of line segment BA; Similarly, the length values of line segments BC, FA and FC are measured.

Make a mobile phone button

Choose points f and c as circles; Point F is the vertical line of AC, which intersects with point H; Select point B and point H in turn to make a mobile button labeled "isosceles triangle". Select two angle values ∠ABG and ∠CBG, click Data | Tabulation, and draw the change table of ∠ABG and ∠CBG values; Draw BA and BC in the same way; FA and FC length value change table. Hide unnecessary objects. Courseware is provided free of charge, and the address is/Rumenji/dengyao-sanjiaoxing.html. It can be downloaded and studied, and I hope it will be helpful to you.