Exercise 38 Page 766

In the given diagram, we have that △ ABC is an isosceles triangle inscribed in ⊙ D.

Since △ ABC is isosceles, we have that AB≅ BC. Then, by the Isosceles Triangle Theorem we also have that ∠ A ≅ ∠ C.

Next, thanks to the Inscribed Angle Theorem we get that the measure of each inscribed angle is half the measure of its corresponding intercepted arc.

Finally, since ∠ A ≅ ∠ C, they have the same measure. This implies that the arcs AB and BC have the same measure as well. m ∠ A = m ∠ C ⇒ 1/2m AB &= 1/2m BC ⇒ m AB &= m BC