First, students will learn what the geometric mean altitude theorem is, and why it's true.

Right Triangle Geometric Mean Altitude Theorem by Anil Kumar

Next, students will learn how to use the geometric mean altitude theorem.

Altitude Geometric Mean Theorem by Mario's Math Tutoring

After that, students will learn what the geometric mean leg theorem is, and why it's true.

Right Triangle Geometric Mean Leg Theorem by Anil Kumar

Next, students will learn how to use the geometric mean leg theorem.

Leg Geometric Mean Theorem by Mario's Math Tutoring

Conclude by giving your students these challenges:

- What's the Weather Like? by NRICH
- Pairs by NRICH
- Opposite Vertices by NRICH
- Coin Star by Pierce School: Problem / Solution

Mentally determine the green angle:

Here's the answer:

The interior angles of a regular hexagon are \(120^\circ,\) and the interior angles of a square are \(90^\circ.\) We know all the angles surrounding the missing angle, plus the angle itself, sum to \(360^\circ.\) Thus, if we remove the known angles, we'll be left with unknown angle. \(120^\circ \cdot 2 = 240^\circ\) and \(240^\circ + 90^\circ = 330^\circ.\) Thus, our missing angle is \(360^\circ - 330^\circ = 30^\circ.\)