1. Lesson 8-4: Arcs and Chords

2. Lesson 8-5: Angle Formulas
Central Angle
Definition:
An angle whose vertex lies on the center of the circle.
Central Angle
(of a circle)
Central Angle
(of a circle)
NOT A Central Angle
(of a circle)
Lesson 8-5: Angle Formulas

3. Lesson 8-4: Arcs and Chords
Theorem #1
Congruent central angles have congruent chords.
Lesson 8-4: Arcs and Chords

4. Lesson 8-4: Arcs and Chords
Theorem #2:
In a circle, congruent chords have congruent arcs. E A B C D
Example:
Lesson 8-4: Arcs and Chords

5. Lesson 8-5: Angle Formulas
Theorem #3
Congruent arcs have congruent central angles. Y Z O
110
Intercepted Arc
Center Angle
Example:
Give is the diameter, find the value of x and y and z in the figure.
Lesson 8-5: Angle Formulas

6. Lesson 8-4: Arcs and Chords
Theorem #4 & #5:
In a circle, chords equidistant from the center are congruent. O A B C D F E
Example:
If AB = 5 cm, find CD.
Since AB = CD, CD = 5 cm.
Lesson 8-4: Arcs and Chords

7. Lesson 8-4: Arcs and Chords
Theorem #6, #7 , #8:
In a circle, if a diameter (or radius) is perpendicular to a chord, then it bisects the chord and its arc. E D A C B
Example:
If AB = 5 cm, find AE.
Lesson 8-4: Arcs and Chords