Geometry Section 10.2 - I can find the measure of arcs in a circle give a central angle and a diameter.

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Presentation transcript:

Geometry Section 10.2 - I can find the measure of arcs in a circle give a central angle and a diameter.

EXAMPLE 1 Find measures of arcs Find the measure of each arc of P, where RT is a diameter. RS a. RTS b. RST c. SOLUTION RS is a minor arc, so mRS = m RPS = 110o. a. RTS is a major arc, so mRTS = 360o 110o = 250o. b. – c. RT is a diameter, so RST is a semicircle, and mRST = 180o.

EXAMPLE 2 Find measures of arcs A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures. Survey a. mAC SOLUTION a. mAC mAB = + mBC = 29o + 108o = 137o

EXAMPLE 2 Find measures of arcs A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures. Survey b. mACD SOLUTION b. mACD = mAC + mCD = 137o + 83o = 220o

EXAMPLE 2 Find measures of arcs A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures. Survey c. mADC SOLUTION mADC mAC = 360o – c. = 360o – 137o = 223o

EXAMPLE 2 Find measures of arcs A recent survey asked teenagers if they would rather meet a famous musician, athlete, actor, inventor, or other person. The results are shown in the circle graph. Find the indicated arc measures. Survey d. mEBD SOLUTION d. mEBD = 360o – mED = 360o – 61o = 299o

EXAMPLE 3 Identify congruent arcs Tell whether the red arcs are congruent. Explain why or why not. a. b. SOLUTION a. CD EF because they are in the same circle and mCD = mEF b. RS and TU have the same measure, but are not congruent because they are arcs of circles that are not congruent.

EXAMPLE 3 Identify congruent arcs Tell whether the red arcs are congruent. Explain why or why not. c. SOLUTION c. VX YZ because they are in congruent circles and mVX = mYZ .