1. 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

2. 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

3. 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

4. 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

5. 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

6. 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.

7. 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

8. 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