Arvold/Dildine

Constructions using Geometer's Sketchpad

Before We Start.

Go to the Display Menu. Choose Preferences.

Check the box Next to AutoShow Labels for Points.

Make sure you are using degrees to measure the angles.

Set the Precisions to Hundreths.

Triangles:

Choose the Point Tool from the menu on the left of the sketch area.
Holding down the shift key (to keep all of the points highlighted) Make three points in the sketch area anywhere.
Make sure all three points are selected (bold) they should be if you held shift down.
Go to the CONSTRUCT Menu and choose Segment.

Now let's measure the angles.

Holding down the shift key choose the three vertexes of the triangle
Go to the MEASURE menu and choose angle. Order is important. Measure all three angles.
Click and Drag the points around and notice the changes in the angles
Go to the MEASURE Menu and choose Calculate. Now choose an angle measure and then + then another angle and so on.
What do you notice about the sum of the triangle angles?

Right Triangle

Choose the Segment tool from the left
Hold Down the shift key and draw a straight horizontal segment
Select an end point and (hold shift) the segment
Select the CONSTRUCT Menu and choose Perpendicular Line
Construct a point on the perpendicular line. Select this point and the other segment endpoint and choose CONSTRUCT Segment
Select the perpendicular line and choose DISPLAY Hide the line
Now construct the final segment and play with this triangle in the same manner as above.
What quality of a right triangle is preserved as you drag this triangle around?

Square:

Select the Segment Tool and construct a horizontal segment
Select a point on this segment and choose Mark Center under the TRANSFORM Menu
Choose the other point and the segment itself and select rotate 90 or -90 (try and see which is best) under the TRANSFORM Menu
Repeat until you have three sides then CONSTRUCT a segment between the two remaining end points.
Drag the vertexes around and see what happens. Select all the vertexes and select CONSTRUCT Polygon Interior. While it is highlighted (wavy) choose Color from under DISPLAY Menu. Have fun.

Extensions:

Can you make an equilateral triangle?
Try making squares on each of the sides of the rt triangle you made. What do you notice about the areas of the squares (hint think pythagorically)?