Visual Proof of the Inscribed Angle Theorem

  • ADMIN M0★ M1 M5

    I hope this visual proof of the Inscribed Angle Theorem will help any of you who prefer diagrams to lengthy text-only proofs!

    Have lots of fun with this cool idea! 🙂

    proof-inscribed-angles-3000.png

    Okay, but that was just a proof for the case when an angle contains a diameter. What about for any old angle? Does it all break down?!?!

    Luckily, the Inscribed Angle Theorem is true for any angle. Take a look at the proof below.

    proof-inscribed-angles-general-case-3000.png

    There's even another case that we haven't covered yet. When the angle has one side that is a tangent to the circle and one side going through the circle (called a secant line), with its vertex still on the circle, its measure is still half of the measure of its inscribed arc.

    proof-inscribed-angles-tangent-secant-case-3000.png

    I really do think we've covered all the cases now! Now, you're all ready to do some geometry problems involving inscribed arcs and angles! 🙂

    Some more visual examples of different inscribed angles: secant-secant inscribed angles, secant-tangent inscribed angles, and tangent-tangent inscribed angles.