Geometry Chapter 10 10 3 APPLY PROPERTIES OF
- Slides: 36
Geometry Chapter 10 10 -3: APPLY PROPERTIES OF CHORDS
Warm-Up
Warm-Up
Warm-Up
Warm-Up
Apply Properties of Chords Objective: Students will be able to solve for lengths and arc measures in circles using the relationships of arcs and chords. Agenda Properties of Chords Corresponding Chords and Arcs Theorems
Properties of Chords Recall that a Chord is a Segment with endpoints on a circle. A chord divides a circle into two arcs
Dividing a Circle Diameter: Divides a circle into two semicircles.
Dividing a Circle Diameter: Divides a circle into two semicircles. Chord: Divides the circle into one minor arc and one major arc.
Theorems with Chords Theorem 10. 3: In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
Example 1
Example 1
Example 1
Example 1
Example 1
Example 1
Theorems with Chords Theorem 10. 4: If one chord is a perpendicular bisector of another chord, then the first chord is a diameter
Theorems with Chords Theorem 10. 5: If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its minor arc.
Example 2
Example 2
Example 3
Example 3
Example 4
Example 4 All three arcs require us to know the value of x.
Example 4
Example 4
Example 4
Theorems with Chords Theorem 10. 6: In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center.
Example 5
Example 5
Example 5
Example 5
Example 6
Example 6
Example 6
Example 6