# Three segments are given.

I need to draw one segment with the same length as any one of the given segments.

Then take the measure of another given segment with my compass and draw a cirlce of that radius from the endpoint of my first segment.

The question is:

1. What is true of any segment that connects this endpoint of the first segment to a point on the circle? Why?

2. Connect both endpoints of the first segment to one of the points where the circles intersect. What is true of the figure you just created? Why?

Truth: The segment created will be the same length as the measure of the given segment: why? it was measured beforehand.

The figure you just created is a triangle with sides congruent to the three segments originally given.

I am not certain of the point of this exercise.

## 1. Any segment that connects the endpoint of the first segment to a point on the circle will have the same length as the measure of the given segment. This is because when you draw a circle with the compass using the measure of the given segment as the radius, any point on the circle will be equidistant from the center of the circle. So, when you connect the endpoint of the first segment to a point on the circle, you are essentially connecting two points that are equidistant from the center of the circle. Therefore, the segment you draw will have the same length as the measure of the given segment.

2. When you connect both endpoints of the first segment to one of the points where the circles intersect, you create a triangle. This triangle will have sides congruent to the three segments originally given. This is because the endpoints of the first segment are connected to the points where the circles intersect, creating two segments that are congruent to the given segments. The remaining side of the triangle is formed by connecting the two points where the circles intersect, which is also congruent to the given segment that was used to create the circles. Therefore, all three sides of the triangle will have the same length as the measure of the given segment.