Objective: Learn
how to construct an isosceles triangle in GSP. Discover properties
of isosceles triangles.
Have students complete this activity using Geometer's Sketchpad.
Sketch and Investigate
1. Construct a circle with center A and control point B.
2. Construct radius AB.
3. Construct radius AC. Drag point C to make sure the radius is attached to the circle.
4. Construct BC.
5. Drag each vertex of your triangle to see how it behaves.
Question 1: Why is the triangle always isosceles?
6. Hide circle AB.
7. Measure the three angles in the triangle.
8. Drag the vertices of your triangle and observe the angle measures.
Question 2: Angle ACB and ABC are the base angles of the isosceles triangle. Angle CAB is the vertex angle. What do you observe about the angle measures?
Explore Further
Investigate the converse of the conjecture you made in question 2: Draw any triangle and measure two angles. Drag a vertex until the two angle measures are equal. Now measure the side lengths. Is the triangle isosceles?
Reference:
Exploring Geometry with the Geometer's Sketchpad by Key Curriculum Press