Download Lesson 8.01 KEY Main Idea (page #) DEFINITION OR SUMMARY

Lesson 8.01 KEY
Main Idea (page #)
Circle (P1)
DEFINITION OR SUMMARY
A CIRCLE IS A SET OF ALL POINTS THAT ARE THE SAME DISTANCE AWAY
FROM A FIXED POINT, CALLED THE CENTER.
CIRCLES ARE NAMED ACCORDING TO THEIR CENTER.
Radius (P1)
Chord of a circle (P1)
EXAMPLE or DRAWING
The name of this circle would be Circle C
THE RADIUS OF A CIRCLE IS THE DISTANCE BETWEEN THE CENTER OF
THE CIRCLE AND A POINT ON THE CIRCLE.
The radius of this circle is CE
Note: All radii are congruent in length
The chord of a circle is a segment on the INTERIOR of a circle
with endpoints ON the circle.
The chord of this circle is AE
THE DIAMETER OF A CIRCLE IS A TYPE OF CHORD THAT PASSES
THROUGH THE CENTER OF THE CIRCLE.
Diameter of a circle (P1)
THE LENGTH OF THE DIAMETER MAY BE FOUND BY DOUBLING THE
LENGTH OF A RADIUS IN THE SAME CIRCLE
The diameter of this circle is DB
THE CIRCUMFERENCE OF A CIRCLE IS THE DISTANCE AROUND
THE CIRCLE FROM ONE POINT BACK TO THE SAME POINT
Circumference (P1)
Arcs (P1)
THE FORMULA USED IS C = PI X D, WHERE PI = 3.14 AND D IS
THE DIAMETER OR C = 2 X PI X R, WHERE PI = 3.14 AND R IS THE
RADIUS.
A MINOR ARC IS IDENTIFIED USING 2 LETTERS AND MEASURES LESS
THAN 180 DEGREES
A MAJOR ARC IS IDENTIFIED USING 3 LETTERS AND MEASURES MORE
THAN 180 DEGREES
ARC LENGTH IS THE DISTANCE BETWEEN 2 POINTS ON THE CIRCLE.
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The circumference measures the red
outline or entire distance around the
circle
Lesson 8.01 KEY
SECANT (P1)
A line that passes through a circle intersecting it at 2 distinct points.
The secant here is FG
Tangent (P1)
A TANGENT IS A LINE THAT INTERSECTS THE CIRCLE IN EXACTLY 1
POINT. THE POINT WHERE THE TANGENT INTERSECTS THE CIRCLE IS
CALLED THE POINT OF TANGENCY
Concentric Circles (P1)
Concentric circles occur when 2 distinct circles share a COMMON
center.
Central Angle and the Arc
(P2)
A CENTRAL ANGLE IS AN ANGLE ON THE INTERIOR, OR INSIDE, OF A
CIRCLE WITH ITS VERTEX AT THE CIRCLE’S CENTER.
THE CENTRAL ANGLE AND ITS INTERCEPTED ARC ARE CONGRUENT.
Semicircle
(P2)
The tangent here is EJ.
Note: The tangent is perpendicular to a
radius of the circle at the point of
tangency.
Angle PTI is 80 degrees so arc
PI is also going to measure 80 degrees
A SEMICIRCLE IS AN ARC WHERE THE CENTRAL ANGLE IS CREATED BY A
DIAMETER OF THE CIRCLE
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Lesson 8.01 KEY
ADJACENT Arcs
(P2)
Arcs that share a common point.
In circle H, AL and LO are adjacent arcs
because they have point L in common
Arc Addition Postulate
(P2)
THE MEASURE OF AN ARC CREATED BY TWO ADJACENT ARCS MAY BE
FOUND BY ADDING THE MEASURES OF THE TWO ADJACENT ARCS.
mAO = 89° + 65°
mAO = 154°
Congruent Arcs Theorem
(P3)
TWO ARCS ARE CONGRUENT IF THE CENTRAL ANGLES THAT INTERCEPT
THEM ARE ALSO CONGRUENT.
Secant Angles
(P4)
WHEN TWO SECANTS INTERSECT, SECANT ANGLES ARE CREATED.
Secant Interior Angle
Theorem
(P4)
THE MEASURE OF A SECANT ANGLE IS EQUAL TO HALF THE SUM OF
THE ARCS IT AND ITS VERTICAL ANGLE INTERCEPT.
m∠WSI = 52° and m∠GSN
= 52°
So, arc IW is congruent to arc NG
Notice <BAN and <MAD are secant
angles.
In the same way, <DAB and <NAM are
secant angles.
Notice the measure of arc
BN is 66 and the measure of arc DM is
78 so in order to find the m<BAN, we
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Lesson 8.01 KEY
add the 2 arcs and divide by 2. We get
66 + 78 = 144 and then dividing by 2, we
get that m<BAN is 72.
Review Note: Remember that m<MAD
would also be 72 because they are
vertical angles.
Inscribed Angle
(P5)
WHEN AN ANGLE IS IN THE INTERIOR OF A CIRCLE AND ITS VERTEX IS A
POINT ON THE CIRCLE, THE ANGLE IS CALLED AN INSCRIBED ANGLE.
< DOG is an inscribed angle
Inscribed Angle Theorem
(P5)
The measure of an inscribed angle is equal to HALF the measure of its
INTERCEPTED arc.
Inscribed Angle to a
Semicircle
(P6)
AN INSCRIBED ANGLE THAT INTERCEPTS A SEMICIRCLE IS A RIGHT
ANGLE.
Congruent Inscribed Angle
Theorem (p7)
TWO OR MORE DISTINCT INSCRIBED ANGLES THAT INTERCEPT THE
SAME ARC, OR CONGRUENT ARCS, ARE CONGRUENT
To find the m<ILK we
need to take half of 94, so 94/2 = 47.
Notice <AED is an inscribed
angle and it equal to 90 degrees because
it intercepts arc AD, which is a
semicircle.
∠OEL and ∠OWL both
intercept arc LO.
m< OEL = m< OWL
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Lesson 8.01 KEY
SECANT-Tangent
Intersection Theorem (P8)
When a secant and tangent intersect at the point of tangency, the
angles created at the point of intersection are half the measurement of
the arcs they intersect.
Line NL is a SECANT. Line IE is TANGENT
to circle S at point N.
m∠LNE = ½ mNAL
80° = ½ mNAL
160° = mNAL
m∠INL = ½ mLPN
100° = ½ mLPN
200° = mLPN
Inscribed Quadrilateral
Theorem (p9)
THE OPPOSITE ANGLES OF AN INSCRIBED QUADRILATERAL TO A CIRCLE
ARE SUPPLEMENTARY
Quadrilateral HAIR is INSCRIBED within
circle Y.
m<HAI + m<IRH = 180 m<RHA + m<AIR
= 180
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Lesson 8.01 KEY
Inscribed angles (p10)
When two inscribed angles intercept the same arc, those angles are
CONGRUENT
m< POM
m< PNM
(3x + 29) = (5x + 7)
EXTERIOR ANGLE TO A
CIRCLE THEOREM (P11)
The angle measure is equal to ½ the
absolute value of the DIFFERENCE of the
measures of their intercepted arcs.
m< = ½(arc 2 – arc 1)
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Lesson 8.01 KEY
Two secants intersect in
the interior of a circle (p11)
The angle measure is equal to ½ the
SUM of the measures of their
intercepted arcs
m< = ½(arc 1 + arc 2)
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