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EXAMPLE 1

In the diagram, P Q , FG JK , and mJK = 80 o . Find mFG. Because FG and JK are congruent chords in congruent circles, the corresponding minor arcs FG and JK are congruent. So , mFG = mJK = 80 o. EXAMPLE 1. Use congruent chords to find an arc measure. SOLUTION.

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EXAMPLE 1

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  1. In the diagram, PQ, FGJK, and mJK= 80o. Find mFG Because FGand JKare congruent chords in congruent circles, the corresponding minor arcs FGand JKare congruent. So, mFG = mJK = 80o. EXAMPLE 1 Use congruent chords to find an arc measure SOLUTION

  2. Use the diagram of D. 1. If mAB = 110°, find mBC Because ABand BCare congruent chords in the same circle, the corresponding minor arcs ABand BCare congruent. So, mBC = mAB = 110o. for Example 1 GUIDED PRACTICE SOLUTION

  3. Use the diagram of D. 2. If mAC = 150°, find mAB for Example 1 GUIDED PRACTICE

  4. ANSWER And, mBC + mAB + mAC = 360° So, 2 mAB + mAC = 360° Because ABand BCare congruent chords in the same circle, the corresponding minor arcs ABand BCare congruent. So, mBC = mAB 2 mAB +150° = 360° 2 mAB = 360 – 150 2 mAB = 210 mAB = 105° mAB = 105° for Example 1 GUIDED PRACTICE SOLUTION Substitute Subtract Simplify

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