G EOMETRY Character builds slowly, but it can be torn down with incredible swiftness. Faith Baldwin Today: Check Up 10.2 Instruction Practice.

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G EOMETRY Character builds slowly, but it can be torn down with incredible swiftness. Faith Baldwin Today: Check Up 10.2 Instruction Practice

G EOMETRY Character builds slowly, but it can be torn down with incredible swiftness. Faith Baldwin Assignment: 10.1 & 10.6 p 821 #1-15, 39-46

C HECK UP For 1 – 3, use circle O. 1. Name a radius. 2. Name a chord. 3. Name a diameter. 4. Is AB tangent to circle C? 5. Find the value of x.

A RCS AND C HORDS Objectives: Know and use properties of arcs of circles Know and use properties of chords of circles Vocabulary: major & minor arc, semicircle, congruent arcs

radius diameter chord secant tangent center

central angle minor arc – connects an angle under 180° major arc – connects an angle over 180° Named by two letters Named by three letters

80° minor arc major arc B C A D major arc = 360 – minor arc Measure of arc equal to measure of central angle.

148° Q R S T Find the measure of each arc: 148° 32° 180° 328°

congruent arcs: arcs of the same measure in either the same circle or congruent circles.

60° A C E congruent arcs: arcs of the same measure in either the same circle or congruent circles. 60° B D

A C E congruent arcs: arcs of the same measure in either the same circle or congruent circles. B D 85° F

In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. AB  CD if and only if AB  CD A B C D

If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc. DE  EF, DG  GF F G E D O If OG is a diameter of circle O, then

Find mBC. 4x° E D C x + 78° B

In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from the center. A F C B AB  CD if and only if EF  EG D G What happens if the segment is also perpendicular?

AB = 12, DE =12, and CE = 7. Find CG. E D C B G A F

Assignment: 10.2 p607 #12-46 even 10.2 A RCS AND C HORDS Optimism is the faith that leads to achievement. Nothing can be done without hope and confidence. Helen Keller

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