Stage 18 · Circles

18.3.4 The Angle Facing a Diameter Is a Right Angle

18.3 The Inscribed Angle Theorem — Seeing the World from On the Circle

Point 4 of 5

18.3.4 The Angle Facing a Diameter Is a Right Angle

Core idea

Look across a diameter and the angle is always 90 degrees — an inscribed angle that spans a semicircle is a right angle, and the reverse holds too.

Module goal. Introduce the inscribed angle, with its vertex on the circle, and establish its half relationship with the central angle plus a run of corollaries — this is the heart of the stage.
eastmath.com · 18.3 The Inscribed Angle Theorem — Seeing the World from On the Circle · 18.3.4 The Angle Facing a Diameter Is a Right Angle