SECTION 10.3Arc and Chords

ANGLE AND ARCS

What is the relationship between arcs and chords?

How can I use the relationship between arcs and chords to solve problems?

TESSELLATION

The rotations of a tessellation can create twelve congruent central angles. Determine whether

TESSELLATIONS

A logo for an advertising campaign is a pentagon that has five congruent central angles. Is ?

How about ?

THEOREM 10.2

Theorem 10.2 – In a circle, or two congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

If Then…

If ,Then…

INSCRIBED/CIRCUMSCRIBED

Inscribed – A polygon with all vertices on the circle:

Circle is circumscribed around ABCD

A B

CD

X

THEOREM 10.3

Theorem 10.3 – In a circle, if a diameter (or radius) is perpendicular to a chord, then it bisects the chord and its arc.

If…Then…And…

EXAMPLE

Circle W has a radius of 10 cm. Radius is perpendicular to chord , which is 16 cm long.

If m, find . Find JL.

EXAMPLE

Circle O has a radius of 25 units. Radius is perpendicular to chord , which is 40 units long.

If find .

Find .

THEOREM

Theorem 10.4 - In a circle, two chords are congruent if and only if they are equidistant from the center.

If Then …

If Then …

EXAMPLE

Chords and are equidistant from the center of . If , and , find and .

HOMEWORK

Page 540 #12 – 34 Even 40 – 43 all

LESSON PLAN

Intro Develop some rules about the relationship

between chords and arcs Standards- 9.3 Supplies – slides, whiteboard, note sheets Timing: One day for notes, one day for a

combined review of 10.3 and 10.4 and a quiz. Day 1:

Essential Questions- slides 2 Input-slides 5 – 7, 10 Guided Practice - slides 3, 4, 8, 9, 11 Independent Practice – Book Work