### Home > CCG > Chapter Ch10 > Lesson 10.1.3 > Problem10-33

10-33.

In $⊙Y$ at right, assume that $m\overarc{ P O }=m\overarc{EK}$. Prove that $\overline{PO} ≅\overline{EK}$. Use the format of your choice.

On circle, Draw line segments from, O, to, Y,  from, K, to, Y, from, E, to, Y, & from, P,  to, Y. Proof: Oval #1: O, Y, = K, Y, =, E, Y, =, P, Y, All Radii are =. (Definition of a circle)

Proof: Oval #2 added in row: arc, P, Q, =, arc, E, K, (Given).

Proof: Oval #3 added in row: angle, P, Y, O, = arc, P, O, (Intercepted arc). Oval #4 added in row: angle, E, Y, K, = arc, E, K, labeled, (Equal Central Angle).

Proof: Oval #5 below right three ovals: angle, P, Y, O, = angle, E, Y, K, (Transitive Property). An arrow from ovals 2, 3, and 4 point to oval 5.

Proof: Oval #6 below the first and second ovals has triangle, P, Y, O, = triangle, E, Y, K, by S, A, S congruency. An arrow from Oval #1 and oval #5 point to Oval #6.

Proof:Oval #7 below Oval #6: segment, P, O, = segment, E, K, (congruent triangle yields congruent parts).