Inscribed Angle Theorem
- Brad Ballinger
Here's a triangle inscribed in a circle.
- It's a triangle.
- Each vertex is on the circle.
- Click the Angle tool, second from the right, to activate it. Its frame will change color to show that it's active.
- Click A, then B, then C. Each point will grow a "halo" to confirm your click. If you click but don't see the halo, try again.
- Click A, then D, then C. (Notice that the Angle tool stays active - so when you want to do something else, pick another tool.)
- Click the Move tool, leftmost on the toolbar, to activate it. Its frame will change color to show that it's active.
- Click and drag A, B, and/or C. Look for relationships between the angle measures that you see.
What do you notice about the measures of and ?
Case 1: D is on a side of the angle.
Do you see any isosceles triangles? How do you know they are isosceles?
Where do isosceles triangles give us congruent angles?
In the figure above, there are (at least) two ways to add onto the teal angle () to make . Which do you see?
Case 2: D is between ray BA and ray BC.
We can apply Case 1 to the tangerine angles. It tells us that . What does Case 1 tell us about the green angles?