u nit 3 circles & lines. s ection 1 key terms w rite down everything you know about circles !
TRANSCRIPT
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UNIT 3Circles & Lines
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SECTION 1Key Terms
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WRITE DOWN EVERYTHING YOU KNOW ABOUT CIRCLES!
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CHORD
Line segment that connects two points on a circle
Chords equidistant from the center are congruent
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DIAMETER & RADIUS
Diameter: Chord passing through the center of the circle
Radius: Line segment from the center to the circumference (outside)
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TANGENT
Line that touches a circle at exactly one point
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SECANT
Line that passes through a circle at two points
What’s the difference between a chord, a tangent, and a secant?
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ARC
Curve that makes up the circle Minor Arc: less than 180° Major Arc: greater than 180° Semicircle: exactly 180° (half the circle)
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CENTRAL ANGLE
Angle whose vertex is on the center of the circle
Measure of a central angle is equal to the measure of the intercepted arc
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EXAMPLE 2
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WRAP UP
Exit Slip Unit 3 Homework Packet
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SECTION 2Chords
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CHORDS & ARCS
Chords intercepting congruent arcs are congruent
Example: Find the measure of arc AC if arc BA = 150°, and arc BA is congruent to arc CB.
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DISTANCE FROM A CHORD TO THE CENTER
Example: What is the length of BD? Hint: What shape do you see in this diagram?
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SECTION 3Tangents
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TANGENTS
How many tangents can you draw that touch both circles at exactly one point?
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TANGENTS ARE PERPENDICULAR TO THE RADIUS THEY INTERSECT
Find the radius.
15
17
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WRAP UP
Exit Slip Homework Packet
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SECTION 4Arc-Angle Relationships
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INSCRIBED ANGLE Angle whose vertex is on the circle
Inscribed angle = Intercepted arc
Example: The measure of arc AC is 80°. Find the measure of AOC and ABC.
12
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ANGLES INSIDE THE CIRCLE
Angle = ½ (Arc 1 + Arc 2) Arc BD = 60° and arc AC = 100 °. Find the
measure of angle AEC.
B
A
C DE
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ANGLES OUTSIDE THE CIRCLE
Angle = ½ (Arc 1 – Arc 2) Chord LP is congruent to chord NM. Arc LP
measures 130°. Arc LN is three times the measure of arc PM. Find the measure of angle PQM.
M
N
L
P
Q
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EXAMPLE
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WRAP UP
Exit Slip Homework Packet
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SECTION 5Segment Product Theorem
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ARCS BETWEEN PARALLEL LINES ARE CONGRUENT
BA
C D
Name the two congruent arcs.
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SEGMENT PRODUCT THEOREM #1
LINES, not angles or arcs! Chord-Chord: AE × EB = CE × ED Example: Find x.
B
A
C DE
9
x
3 6
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SEGMENT PRODUCT THEOREM #2
Tangent-Tangent: CD = AD “Hat Rule” Can you prove this?
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SEGMENT PRODUCT THEOREM #3
Tangent-Secant: PA2 = PB × PC Example: If PB is 2 inches and BC is 16
inches, find PA.
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SEGMENT PRODUCT THEOREM #4
Secant-Secant: BE × AE = DE × CE Example: If AB = 5, CD = 10, and DE = 12,
what is the length of BE?
D
BE
A
C
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WRAP UP
Exit Slip Homework Packet Due Friday Unit 3 Test Friday