# Central Angles, Inscribed Angles, and their Intercepted Arcs

This lesson is to be used to discover relationships between central angles, inscribed angles and the measure of the intercepted arc.
Follow the directions and answer the questions below.

**Directions:**
o Check on the checkbox to Show Central Angle and its Measure
o Check on the checkbox to Show Arc and its Measure
o Drag points C and D and record at least three measures:

- < 180
^{o} ^{ }= 180^{o}- > 180
^{o}^{}

**Make a conjecture about the relationship between a central angle and its intercepted arc:**

**Directions:**
o Check on the checkbox to Show Inscribed Angle and its Measure
o Drag points E, C and D and record at least three measures:

- < 180
^{o} ^{ }= 180^{o}- > 180
^{o}^{}

**a) Make a conjecture about the relationship between a central angle and an inscribed angle. b) Make a conjecture about the relationship between an inscribed angle and its interecepted arc.**