10.5 Apply Other Angle Relationships in Circles … · Foldable: Geometry Notes Name _____ 10.5...
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10.5 Apply Other Angle Relationships in Circles +JMJ 1. m!1 = ______ 2. mAB ! = _______ 3. x = _______ 4. x = _______ 5. x = _______________ 6. x = ________________ 7. y = ________________ Challenge Problems:
Transcript of 10.5 Apply Other Angle Relationships in Circles … · Foldable: Geometry Notes Name _____ 10.5...
10.5 Apply Other Angle Relationships in Circles +JMJ
Geometry Notes Name ________________ 10.5 Apply Other Angle Relationships in Circles Recall …. You know that the measure of a central angle ______________ its intercepted arc. You know that the measure of an inscribed angle is ______________ of its intercepted arc.
ANGLES ON THE CIRCLE THEOREM
If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.
!1 intercepts arc ________ m!1 =__________________ !2 intercepts arc _________ m!2=__________________
1. m!1 = ______
2. mAB! =_______
ANGLES INSIDE THE CIRCLE THEOREM
If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
!1 intercepts arcs ________________ m!1 =__________________ !2 intercepts arcs _______ m!2=_________________
3. x =_______
4. x =_______
Geometry Notes Name ________________ 10.5 Apply Other Angle Relationships in Circles Recall …. You know that the measure of a central angle ______________ its intercepted arc. You know that the measure of an inscribed angle is ______________ of its intercepted arc.
ANGLES ON THE CIRCLE THEOREM
If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.
!1 intercepts arc ________ m!1 =__________________ !2 intercepts arc _________ m!2=__________________
1. m!1 = ______
2. mAB! =_______
ANGLES INSIDE THE CIRCLE THEOREM
If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
!1 intercepts arcs ________________ m!1 =__________________ !2 intercepts arcs _______ m!2=_________________
3. x =_______
4. x =_______
ANGLES OUTSIDE THE CIRCLE THEOREM If a tangent and a secant, two tangents, or two secants intersect outside a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.
Tangent & Secant: !1 intercepts arcs________ m!1 =_________________
Two Tangents: !2 intercepts arcs _______ m!2=_________________
Two Secants:
!3 intercepts arcs________ m!3=__________________
5. x =_______________
6. x =________________
7. y = ________________
Challenge Problems: 8. Find x and y.
9. Find x.
Foldable:
Geometry Notes Name ________________ 10.5 Apply Other Angle Relationships in Circles Recall …. You know that the measure of a central angle ______________ its intercepted arc. You know that the measure of an inscribed angle is ______________ of its intercepted arc.
ANGLES ON THE CIRCLE THEOREM
If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.
!1 intercepts arc ________ m!1 =__________________ !2 intercepts arc _________ m!2=__________________
1. m!1 = ______
2. mAB! =_______
ANGLES INSIDE THE CIRCLE THEOREM
If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
!1 intercepts arcs ________________ m!1 =__________________ !2 intercepts arcs _______ m!2=_________________
3. x =_______
4. x =_______
Geometry Notes Name ________________ 10.5 Apply Other Angle Relationships in Circles Recall …. You know that the measure of a central angle ______________ its intercepted arc. You know that the measure of an inscribed angle is ______________ of its intercepted arc.
ANGLES ON THE CIRCLE THEOREM
If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.
!1 intercepts arc ________ m!1 =__________________ !2 intercepts arc _________ m!2=__________________
1. m!1 = ______
2. mAB! =_______
ANGLES INSIDE THE CIRCLE THEOREM
If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle.
!1 intercepts arcs ________________ m!1 =__________________ !2 intercepts arcs _______ m!2=_________________
3. x =_______
4. x =_______
ANGLES OUTSIDE THE CIRCLE THEOREM
If a tangent and a secant, two tangents, or two secants intersect outside a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.
Tangent & Secant: !1 intercepts arcs________ m!1 =_________________
Two Tangents: !2 intercepts arcs _______ m!2=_________________
Two Secants:
!3 intercepts arcs________ m!3=__________________
5. x =_______________
6. x =________________
7. y = ________________
Challenge Problems: 8. Find x and y.
9. Find x.
