Lesson 8.01

Main Idea (page #) / DEFINITION OR SUMMARY / EXAMPLE or DRAWING
Circle (P1) /
The name of this circle would be Circle C
Radius (P1) /
The radius of this circle is CE
Note: All radii are congruent in length
Chord of a circle (P1) / The chord of a circle is a segment on the ______of a circle with endpoints ______the circle. /
The chord of this circle is AE
Diameter of a circle (P1) /
The diameter of this circle is DB
Circumference (P1) /
The circumference measures the red outline or entire distance around the circle
Arcs (P1) /
______(P1) / A line that passes through a circle intersecting it at 2 distinct points. / The secant here is FG
Tangent (P1) / The tangent here is EJ.
Note: The tangent is perpendicular to a radius of the circle at the point of tangency.
Concentric Circles (P1) / Concentric circles occur when 2 distinct circles share a ______center. /
Central Angle and the Arc
(P2) / Angle PTI is 80 degrees so arc PI is also going to measure 80 degrees
Semicircle
(P2) /
______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) /
mAO = 89° + 65°
mAO = 154°
Congruent Arcs Theorem
(P3) / m∠WSI = 52° and m∠GSN = 52°
So, arc IW is congruent to arc NG
Secant Angles
(P4) / Notice <BAN and <MAD are secant angles.
In the same way, <DAB and <NAM are secant angles.
Secant Interior Angle Theorem
(P4) / 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 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) / < DOG is an inscribed angle
Inscribed Angle Theorem
(P5) / The measure of an inscribed angle is equal to ______the measure
of its ______arc. / To find the m<ILK we need to take half of 94, so 94/2 = 47.
Inscribed Angle to a Semicircle
(P6) / Notice <AED is an inscribed angle and it equal to 90 degrees because it intercepts arc AD, which is a semicircle.
Congruent Inscribed Angle Theorem (p7) / ∠OEL and ∠OWL both intercept arc LO.
m< OEL __ m< OWL
______-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______. Line IE is ______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) /
Quadrilateral HAIR is ______within circle Y.
m<HAI + m<IRH = 180 m<RHA + m<AIR = 180
Inscribed angles (p10) / When two inscribed angles intercept the same arc, those angles are ______/
m< POM m< PNM
(3x + 29) = (5x + 7)
/ The angle measure is equal to ½ the absolute value of the ______of the measures of their intercepted arcs.
m< = ½(arc 2 – arc 1)
Two secants intersect in the interior of a circle (p11) / / The angle measure is equal to ½ the ______of the measures of their intercepted arcs
m< = ½(arc 1 + arc 2)

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