## Act 1

1. Where will the arena be located?

2. Write down a guess.

Here is a Desmos Activity that helps with gathering student guesses. Use the overlay feature to display all the estimates at once.

## Act 2

3. What information would be useful to figure this out?

4. Write down some questions you have in your head right now.

I’m excited to see where Desmos goes with their Geometry tool because this lesson could really fit nicely into Activity Builder (see link in Act 1). Until then, students can work with this image to use constructions to try to find the equidistant point.

In addition to constructions, students can work and reason with this graph image.

Possible actions include calculating the distance between points, midpoints, and writing and graphing perpendicular equations based on the information gathered.

Here is a handout with the images.

## Act 3

**Common Core Standards**

HSG.CO.C.10

Prove theorems about triangles.

HSG.CO.D.12

Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

**TEKS**

G.5(C)

use the constructions of congruent segments, congruent angles, angle bisectors, and perpendicular bisectors to make conjectures about geometric relationships

G.6(D)

verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems