**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