Chord, Angle and Arc
Let's put on our explorer hats! Take point B for a spin around the circle and keep a keen eye on angle B.
- What fascinating connections do you notice between angle B and the central angle?
- What's the sum of the angles on the arc e and its alternate arc d, determined by points C and D?
Let's sum up our discoveries! As we've journeyed through the above activity, we've unveiled a fascinating rule: the angle formed by any arc on the alternate arc is always half of the angle formed at the center. Not just that – all angles made by an arc on the alternate arc are equal! We also discovered that that the sum of the angles on the arc e and its alternate arc d, determined by points C and D is 180°. So, to wrap it up: angles on the alternate arc are equal, and pairs on an arc and its alternate are always supplementary (Pairs of angles of sum 180° are usually called supplementary angles). Now, share your thoughts on this geometric revelation!