First, we will show that if ∠ BAC and ∠ DAE are congruent angles, then BC≅ DE. Let's consider the given diagram.
We can see that ∠ BAC and ∠ DAE are the central angles of BC and DE, respectively. Recall that the measure of a minor arc is the measure of its central angle.
m∠ BAC = mBC and m∠ DAE = mDE
We know that ∠ BAC ≅ ∠ DAE. Therefore, by the definition of congruent angles, we can say that their angle measures are the same.
m∠ BAC = m∠ DAE
Now, we can substitute mBC and mDE for m∠ BAC and m∠ DAE, respectively into the above equation.
m∠ BAC = m∠ DAE
⇓
mBC = mDE
Finally, by the definition of congruent arcs, since BC and DE have the same measure, they are congruent.
BC ≅ DE
Let's summarize the above process in a flow proof.
b In this part, we will prove that if the arcs are congruent, then their central angles are congruent. Consider the same diagram as in Part A.
Proceeding in the same way as we did in Part A, we can write flow proof.
