# Isosceles Triangle

- Author:
- Sarah Keistler

## Isosceles Triangle

I found three different ways to construct isosceles triangles. For a triangle to be isosceles it has two sides of equal lengths and two angles of equal measure.
First we construct circle A using the circle tool. Then we construct the radius AB using the segment tool. Then we also construct radius AC with C being a point anywhere on the circle. Then using the segment tool we can construct segments AB, BC, CA to form triangle ABC. When we measure the angles measures and the side lengths of the triangle and see that the measures of and are equal and CA and AB are equal. Therefore triangles ABC is isosceles. We can move point C anywhere along the circle and the triangle is still an isosceles triangle.
We can also construct a isosceles triangle with a segment. Construct segment DE and point F not on DE. Then we will reflect point F over segment DE to form F'. Using the segment tool we construct DF FF' and F'D. This forms triangle DFF'. Using the angle measure tool we can see that the measures of and are equal. Also we can see from the distance tool that DF and DF' are equal. Therefore triangle DFF' is an isosceles triangle. We can observe that if we move point F the triangle remains an isosceles triangle.
Lastly we can construct an isosceles triangle using rays. First we construct ray GH and GI. Then we construct the angle bisector of . Using the point tool we constructed point J that lies on the angle bisector. Next we construct a line perpendicular to the angle bisector and through point J. The point of intersection between the perpendicular line and ray GH is labeled K and the point of intersection between the perpendicular line and ray GI is labeled L. We then use the segment tool to construct lines KL, LG, and GK. This forms triangle KLG. We can use the angle measure tool to see that and have equal measure and that segments GK and GL have equal length. Therefore we can conclude that triangle KLG is an isosceles triangles. We can move point G and observe that the triangle remains an isosceles triangle.