### Home > CCG > Chapter 10 > 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, Reason, (Definition of a circle)

Added to proof: Oval #2, measure of arc, P, O, = measure of arc, E, K, reason, given.

Added to proof: Oval #3, measure of angle, P, Y, O, = measure of arc, P, O, & Oval #4, measure of angle, E, Y, K, = measure of arc, E, K , reason for each, definition of measure of an arc.

Added to proof: Oval #5, measure of angle, P, Y, O, = measure of angle, E, Y, K, reason transitive property, arrows from ovals #2, 3, & 4, point to oval #5.

Added to proof: Oval #6, triangle, P, Y, O, is congruent to triangle, E, Y, K, reason, S, A, S, congruency, Arrows from oval #1, & from oval #5, point to oval #6.

Added to proof: Oval #7, segment, P, O, is congruent to segment, E, K, reason, congruent triangles give congruent parts.