Refer to the figure below. Given that AC and BD are diameters of ⊙O, prove that AB is congruent to CD.
What is the relationship between ∠AOB and ∠DOC?
∠AOB and ∠DOC are vertical angles are therefore congruent. By the Angle-Chord Theorem, AB is congruent to CD.
Suppose AB is a chord of ⊙O and CD is a chord of ⊙P. Is it true that if AB = CD, then ⊙O is congruent to ⊙P?
Read the Angle-Chord Theorem and the Arc-Chord Theorem carefully.
Given a circle with radius r, what is the maximum length of a chord of that circle?
In other words, how far apart can two points be while still being on the same circle?
All chords are diameters, but not all diameters are chords. True or false?
Review the definitions of chord and diameter.
If two chords in the same circle are not congruent, then their associated arcs are also not congruent. True or false?
Check out the Arc-Chord Theorem.
Make it rain.