# Thales Theorem: Exploration

## Construct a circle, diameter and inscribed angle

Construct A with diameter BC. Construct inscribed angle BDC

## Use this space to perform the following construction.

1. Construct A
2. Construct diameter BC
3. Construct inscribed angle: BDC
4. Use the angle measurement tool to find
4.a. mDBC
4.b. mDCB

## Without using the angle measurement tool, compute the the measure of the inscribed angle

Without using the measurement tool, use your knowledge of the interior angles of triangle BCD to compute the inscribed angle: BDC.

## Move point D around circle A to at least three new positions.

What is the measure of BDC at each of the three new positions?

## Why?

Try to explain, in your own words, the measure of an angle inscribed from the diameter of a circle.