TODAY IN GEOMETRY…

Warm Up: Major and Minor Arcs

Learning Target : 10.3 You will use relationships of arcs and chords in a circle.

Independent practice

WARM UP: Identify the arcs as a minor, major or semicircle. Then given the measurement of the arcs.

𝐸

𝐴

𝐶87 °

𝐵

𝐷

93 °

83 °72 °25 °

1.

2.

3.

4.

Minor,

Semicircle,

Major,

Minor,

PROPERTIES OF CHORDS(3)

PROPERTIES OF CHORDS(1): In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

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𝐵 𝐶

𝐷

EXAMPLE:

PRACTICE:

3. If the measure of arc , find the measure of arc .

SOLUTIONS1. Measure of arc BC is 2. Measure of arc AB is 3. Measure of arc ABC is

PROPERTIES OF CHORDS(2): If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.

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𝐷

𝐶

𝐵

𝐸

EXAMPLE:

PRACTICE:

The diameter bisects a chord, therefore the arcs are congruent:

Add

Divide

9 𝑥=9 (8 )=72 ° 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜𝑎𝑟𝑐𝐶𝐷=72° 𝑑𝑜𝑢𝑏𝑙𝑒𝑎𝑟𝑐𝐶𝐷=2 (72 )=144 °

PROPERTIES OF CHORDS(3): If two chords are congruent, then they are equidistant from the center.

𝐴

𝐵 𝐶

𝐷

𝐸

𝐹 𝐺

EXAMPLE:

𝑒𝑞𝑢𝑎𝑙 𝑡𝑜𝑆𝑇=𝟑𝟐 h𝑎𝑙𝑓 𝑜𝑓 𝑄𝑅=𝟏𝟔 Use Pythag. Thrm:

Radius

PRACTICE:

The two chords are congruent, therefore they are equidistant from the center:

Subtract

Divide

Substitute back into equation for

HOMEWORK #3:

Pg. 667: 3-15

If finished, work on other assignments:

HW #1: Pg. 655: 3-20, 24-26, 30HW #2: Pg. 661: 3-14, 17, 23