THEOREM 10.3 B C In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.
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1 10.3 Your Notes pply Properties of hords oal p Use relationships of arcs and chords in a circle. HOM 10.3 In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. > if and only if >. xample 1 Use congruent chords to find an arc measure In the diagram, ( > (, >, and m ind m ecause and are congruent in congruent, the corresponding minor arcs and are. So, m 5 m 5. HOM 10.4 If one chord is a perpendicular bisector of another chord, then the first chord is a diameter. If QS is a perpendicular bisector of, then diameter of the circle. S P is a HOM 10.5 If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc. If is a diameter and, then H > H and >. H opyright Holt Mcougal. ll rights reserved. Lesson 10.3 eometry Notetaking uide 275
2 10.3 Your Notes pply Properties of hords oal p Use relationships of arcs and chords in a circle. HOM 10.3 In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. > if and only if >. xample 1 Use congruent chords to find an arc measure In the diagram, ( > (, >, and m ind m ecause and are congruent chords in congruent circles, the corresponding minor arcs and are congruent. So, m 5 m HOM 10.4 If one chord is a perpendicular bisector S of another chord, then the first chord P is a diameter. If QS is a perpendicular bisector of, then QS is a diameter of the circle. HOM 10.5 If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc. If is a diameter and, then H > H and >. H opyright Holt Mcougal. ll rights reserved. Lesson 10.3 eometry Notetaking uide 275
3 o find the center of a given circle, choose three points on the circle. hen use the method in xample 2 to find xample 2 Use perpendicular bisectors Journalism journalist is writing a a story about three sculptures, arranged as shown at the right. Where should the journalist place a camera so that it is the same distance from each sculpture? Step 1 Label the sculptures,, and. raw segments and. Step 2 onstruct the of and. Step 3 ind the point where these bisectors. his is the center of the circle through,, and, and so it is from each point. amera xample 3 Use a diameter Use the diagram of ( to find the length of. ell what theorem you use. iameter is to. So, by heorem 10.5,, and 5. herefore, 5 2( ) 5 2( ) 5. HOM 10. In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from > if and only if Lesson 10.3 eometry Notetaking uide opyright Holt Mcougal. ll rights reserved.
4 o find the center of a given circle, choose three points on the circle. hen use the method in xample 2 to find xample 2 Use perpendicular bisectors Journalism journalist is writing a a story about three sculptures, arranged as shown at the right. Where should the journalist place a camera so that it is the same distance from each sculpture? Step 1 Label the sculptures,, and. raw segments and. Step 2 onstruct the perpendicular bisectors of and. Step 3 ind the point where these bisectors intersect. his is the center of the circle through,, and, and so it is equidistant from each point. amera xample 3 Use a diameter Use the diagram of ( to find the length of. ell what theorem you use. iameter is perpendicular to. So, by heorem 10.5, bisects, and 5. herefore, 5 2( ) 5 2( ) HOM 10. In the same circle, or in congruent circles, two chords are congruent if and only if they are equidistant from > if and only if Lesson 10.3 eometry Notetaking uide opyright Holt Mcougal. ll rights reserved.
5 xample 4 Use heorem 10. In the diagram of (, ind. hords and are congruent, so by heorem 10. they are from. herefore, x 2 8 3x 12 5 Use heorem x 5 Substitute. x 5 Solve for x. So, 5 3x 5 3( ) 5. heckpoint omplete the following exercises. 1. If m V , find m S. S V 2. ind the measures of,, and. 4x8 (80 2 x)8 Homework 3. In the diagram in xample 4, suppose 5 27 and ind. opyright Holt Mcougal. ll rights reserved. Lesson 10.3 eometry Notetaking uide 277
6 xample 4 Use heorem 10. In the diagram of (, ind. hords and are congruent, so by heorem 10. they are equidistant from. herefore, x 2 8 3x 12 5 Use heorem x 5 7x 2 8 Substitute. x 5 2 Solve for x. So, 5 3x 5 3( 2 ) 5. heckpoint omplete the following exercises. 1. If m V , find m S. m S S V 2. ind the measures of,, and. m 5 48, m 5 48, m x8 (80 2 x)8 Homework 3. In the diagram in xample 4, suppose 5 27 and ind opyright Holt Mcougal. ll rights reserved. Lesson 10.3 eometry Notetaking uide 277
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