**Review**

- Circle Size
- A circle’s size depends on the length of its radius
- The larger the radius, the larger the circle, and vice versa
- Two circles are congruent if they have congruent radii (same length)

- Central Angles
- Are measured in degrees
- Are formed by two radii
- Produce minor arcs along the circle’s circumference

- Minor Arcs
- The measure of a minor arc equals the measure of the central angle that intercepts it.
- The radii from the minor arc’s two endpoints form the sides of the central angle.
- A segment connects the minor arc’s two endpoints for a chord.

- Chords
- A chord is a segment with both endpoints on a circle.
- If two chords are the same distance from the center of a circle, then they are congruent.

- Arcs
- An arc is part of a circle with two endpoints.

**Notes**

- Arc Length and Central Angle Measure
- Notice that the arcs in this video have different lengths (in units), yet their central angles have the same measure (in degrees).

- Congruent Arcs
- Both of the following rules MUST be true for arcs to be congruent:
- They have the same measure.
- They must belong to the same circle or congruent circles.

- Both of the following rules MUST be true for arcs to be congruent:

- Congruent Minor Arcs Have Congruent Chords
- If the associated chords of two arcs are congruent, then the arcs are congruent.
- Converse: If two arcs are congruent, then their associated chords are congruent.
- Here’s the proof. Copy it down using the template below.

- Chords and Central Angles
- Two chords are congruent if and only if their associated central angles are congruent.
- Two central angles are congruent if and only if their associated chords are congruent.

**Examples**

- Ex 1. Given below, the arcs and must be congruent.

- Ex 2. Given below, if and are congruent, what is the measure of ?
- Because central angles are congruent if their corresponding arcs are congruent, =68°.

- Ex 3. Given below, if and are congruent, what is the measure of ?
- Since a circle measures 360, subtract the given angle (60°) to see what’s left? You get 300°.
- Since both arcs are congruent, divide 300° by 2 to get 150° each.

- Ex 4. Given below, if and are congruent, what is the measure of chord ?
- When two arcs are congruent, their associated chords are congruent, so .

- Ex 5. For two arcs to be congruent, they must be in the same circle or congruent circles and they must have the same central angle measure.

- Ex 6. If chord is congruent to chord , what is the measure of ?
- Since the chords are congruent, the corresponding arcs are congruent. The central angles of those arcs are the same measure as those arcs, so the answer is 116°