Assignment 1: 10.3 WB Pg. 127 #1 – 14 all 10.3 Arcs and Chords Assignment 1: 10.3 WB Pg. 127 #1 – 14 all

Arcs and Chords Theorem 10.2: In the same circle or in congruent circles: 1. Congruent arcs have congruent chords 2. Congruent chords have congruent arcs U T R S O 𝐼𝑓 𝑇𝑈 ≅ 𝑅𝑆 𝑡ℎ𝑒𝑛, 𝑇𝑈 ≅ 𝑅𝑆 -or- 𝐼𝑓 𝑇𝑈 ≅ 𝑅𝑆 𝑡ℎ𝑒𝑛, 𝑇𝑈 ≅ 𝑅𝑆

Theorem 10.3 If diameter (or radius) is perpendicular to a chord, then it bisects the chord and its arc. C 𝐼𝑓 𝐶𝐷 ⊥ 𝐴𝐵 𝑡ℎ𝑒𝑛, 𝐴𝐷 ≅ 𝐵𝐷 𝑎𝑛𝑑 𝐴𝑍 ≅ 𝐵𝑍 O A B Z D

Theorem 10.4 The perpendicular bisector of a chord is a diameter (or radius) of the circle. C 𝐼𝑓 𝐶𝐷 ⊥ 𝐴𝐵 𝑎𝑛𝑑 𝐴𝑍 ≅ 𝐵𝑍 𝑡ℎ𝑒𝑛 𝐶𝐷 𝑖𝑠 𝑡ℎ𝑒 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 C O A B Z D

Theorem 10.5 In the same circle or congruent circles, two chords are congruent iff they are equidistant from the center. J 𝐼𝑓𝑋𝐿=𝑌𝐿 𝑡ℎ𝑒𝑛, ≅ 𝐹𝐺 ≅ 𝐽𝐻 Y F L -or- H 𝐼𝑓 𝐹𝐺 ≅ 𝐽𝐻 𝑡ℎ𝑒𝑛,𝑋𝐿=𝑌𝐿 X G

Examples In the diagrams that follow, O is the center of the circle. 1. Y M 5 X 3 O P M Q O 13 2.

Examples In the diagrams that follow, O is the center of the circle. 3. 120° B O D C 4. A B C O D

Examples In the diagrams that follow, O is the center of the circle. 5. A B O C 6. D M E O N F C