9-5 Inscribed Angles - teachers.henrico.k12.va.us

9-5 Inscribed Angles - teachers.henrico.k12.va.us

8-5 Angles in Circles Central Angles A central angle is an angle whose vertex is the CENTER of the circle Central Angle (of a circle) Central Angle (of a circle) NOT A Central

Angle (of a circle) CENTRAL ANGLES AND ARCS The measure of a central angle is equal to the measure of the intercepted arc. CENTRAL ANGLES AND ARCS The measure of a central angle is equal to the measure of the intercepted arc. Central Y Angle 110 0

11 O Z Intercepted Arc EXAMPLE Segment AD is a diameter. Find the values of x and y and z in the figure. 25 B C

A x y O z 55 D x = 25 y = 100 z = 55 SUM OF CENTRAL ANGLES The sum of the measures fo the central angles of a circle with

no interior points in common is 360. 360 Find the measure of each arc. D 2x -14 C 4x 3x

0 +1 3x E 2x 4x + 3x + 3x + 10+ 2x + 2x 14 = 360 x = 26 A 104, 78, 88, 52, 66 degrees B

Inscribed Angles An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords. 1 Is NOT! 2 Is SO! 3 Is

NOT! 4 Is SO! Thrm 9-7. The measure of an inscribed angle is INSCRIBED ANGLE THEOREM equal to the measure of the intercepted arc. The measure of an inscribed angle is equal to the measure of the intercepted arc.

Thrm 9-7. The measure of an inscribed angle is INSCRIBED ANGLE THEOREM equal to the measure of the intercepted arc. The measure of an inscribed angle is equal to the measure of the intercepted arc. 1 2

Thrm 9-7. The measure of an inscribed angle is INSCRIBED ANGLE THEOREM equal to the measure of the intercepted arc. The measure of an inscribed angle is equal to the measure of the intercepted arc. Inscribed Angle 0 11 55

Y Z Intercepted Arc Thrm 9-7. Thethe measure of an Find value ofinscribed x and angle y is equal to the measure of the intercepted arc.

in the figure. X = 20 P 40 Q S 50 y x T

R Y = 60 Corollary 1. Ifthe two inscribed intercept Find value ofangles x and y the same arc, then the angles are congruent.. in the figure.

P y X = 50 Q Y = 50 S 50 x T R

An angle formed by a chord and a tangent can be considered an inscribed angle. An angle formed by a chord and a tangent can be considered an inscribed angle. P Q S R mPRQ = mPR What is mPRQ ? P

Q S 60 R An angle inscribed in a semicircle is a right angle. P 180 R

An angle inscribed in a semicircle is a right angle. P S 180 90 R Interior Angles Angles that are formed by two intersecting chords. (Vertex IN the circle) A

D B C Interior Angle Theorem The measure of the angle formed by the two chords is equal to the sum of the measures of the intercepted arcs. Interior Angle Theorem The measure of the angle formed by the two chords is equal to the sum of the measures of the intercepted arcs. A

D 1 B C 1 m1 (mAC mBD) 2 Interior Angle Theorem A 91 C

y x B D 85 1 x (91 85) 2 x 88 y 180 88 y 92

Exterior Angles An angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside the circle. (vertex OUT of the circle.) Exterior Angles An angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside the circle. k j 1 k

j 1 k j 1 Exterior Angle Theorem The measure of the angle formed is equal to the difference of the intercepted arcs. k j

1 k j 1 1 m1 (k j) 2 k j

3 Find mACB

PUTTING IT TOGETHER! D 6 C E A 3 Q 2 1 5

4 G F AF is a diameter. mAG=100 mCE=30 mEF=25

Find the measure of all numbered angles. Inscribed Quadrilaterals If a quadrilateral is inscribed in a circle, then the opposite angles are supplementary. P Q mPSR + mPQR = 180 S R

Recently Viewed Presentations

  • 1 The MindReading Agency Predictive Market on the

    1 The MindReading Agency Predictive Market on the

    The MindReading Agency Predictive Market on the 2007 MRS Papers A Market Research Project by BrainJuicer. Produced March 07 Flow of the Juicer A Diverse Group of 575 people in media, research, planning and marketing Predictive Markets - A Fresh...
  • Strategic Planning Celebration 2013 - SJECCD

    Strategic Planning Celebration 2013 - SJECCD

    Number of New Jobs by Sector2011 to 2022. 2011 Jobs Professional, Scientific, and Technical Services Ambulatory Health Care Services Educational Services (Private)
  • 210 plants, capacity of 14.18 bil. gal. - Pork Checkoff

    210 plants, capacity of 14.18 bil. gal. - Pork Checkoff

    210 plants, capacity of 14.18 bil. gal. Cellulosic: 16.9 mil. gal. - 1% of the total. 346 mil. gal. still under construction. Full output would use 5.05 bil. bu. of ...
  • DBQ Powerpoint II - rhsweb.org

    DBQ Powerpoint II - rhsweb.org

    Relevant thesis develops ALL parts of the question in an original way. Samples… U.S. overseas expansion was seen as imperialistic by some yet other Americans viewed the practice as a necessary evolution of the American identity from an insular self-sufficient...
  • Plastic Fantastic For some time now, plastics have

    Plastic Fantastic For some time now, plastics have

    These polymers possess a delocalised pi-electron system along their backbone that confers semiconducting properties to the polymer. * Researchers have discovered that conjugated polymers, which have a pathway of alternating double and single bonds, exhibit metallic and semiconductor characteristics.
  • A Career in Architecture - madison-lake.k12.oh.us

    A Career in Architecture - madison-lake.k12.oh.us

    A Career in Architecture Architecture What is Architecture? About Architecture Design Architects Project Architects Construction Managers Draftspersons Landscape Architects What is Architecture? "Architecture is the thoughtful making of space." - Louis Kahn What is Architecture?
  • J.Griffin On Human Rights Oxford University Press 2008

    J.Griffin On Human Rights Oxford University Press 2008

    Second Step: personhoodas non-abstractautonomy «Ouraim must be the more modestone of understanding ….the autonomyof Homo sapiens. ... the solution is to advance a non-naturalistic (not based on natural sciences) notion of «human nature, agents» !
  • Human Population Growth

    Human Population Growth

    Quickly growing populations can be represented by a special line graph called a SIGMOID (S-shaped) curve. A (Lag phase)- the population has few individuals that are reproducing slowly at first. ... These factors rarely end a population, but takes them...