Definition
An inscribed angle is an angle whose vertex lies on a circle and whose sides contain chords of the circle.
Why It Matters
Inscribed angles reveal crucial symmetry relationships inside a circle. The fact that any angle in a semicircle is a right angle is a valuable design shortcut in geometry and carpentry.
Core Concepts
- Inscribed Angle Theorem: The measure of an inscribed angle is exactly half the measure of its intercepted arc.
- Thales’ Theorem: An angle inscribed in a semicircle is always a right angle ().
- How to read: “The measure of ninety degrees.”
- Meaning: If an inscribed angle intercepts a diameter, it forms a right angle.
- Common Arc Theorem: Inscribed angles that intercept the same arc are congruent.