Page 161 - Math Course 3 (Book 2)
P. 161

Circles: Arcs and Chords





                                                                    Your Turn!
                   Answer

                                                                   Prove Theorem 11.2
                Statements                    Reasons
                                                                    PROOF
                1. DE ≅ FG; m∠EBF = 24;                             Choose the best reason to complete the following
                    DFG is a semicircle.      1. Given              proof.
                                                                    Given:  AB ≅ EF
                2. mDFG = 180                 2. Def. of semicircle
                                                                            AB ≅ CD
                                              3. In a circle, if 2
                3. DE ≅ FG                         chords are ≅, corr.    Prove:  CD ≅ EF
                                                   minor arcs are ≅.
                                                                               A                B
                4. mDE = mFG                  4. Def. of ≅ arcs
                                                                            C                       F
                                              5. Def. of arc
                5. mEF = 24
                                                   measure
                                              6. Arc Addition
                6. mED + mEF + mFG = mDFG
                                                  Postulate
                                                                               E                D
                7. mFG + 24 + mFG = 180       7. Substitution

                                              8. Subtraction
                8. 2(mFG) = 156                    Property  and    Statements            Reasons
                                                   simplify         1. AB ≅ EF; AB ≅ CD   1. Given
                9. mFG = 78                   9. Division Property                        2. In a circle, 2 minor
                                                                    2. AB ≅ EF            arcs are ≅, chords are ≅
                                              10. Def. of arc
                10. mFG = m∠FBG
                                                     measure        3. CD ≅ EF            3. ___________
                11. m∠FBG = 78                11. Substitution.                           4. In a circle, 2 chords
                                                                    4. CD ≅ EF
                                                                                          are ≅, minor arcs are ≅.
                                                                    A. Segment Addition Postulate
                                                                    B. Definition of ≅
               Standardized text Example                            C. Definition of Chord
                                                                    D. Transitive Property
                 A regular hexagon is drawn in a circle as part of a
                 logo for an advertisement. If opposite vertices are   Answer
                 connected by line segments, what is the measure
                 of angle P in degrees?                           Standardized text Example

                                            A                      ADVERTISING
                                                                   A logo for an advertising campaign is a pentagon
                                                                   that has five congruent central angles. Determine
                                          P                        whether                          A
                                                  B
                                                                   A. yes
                                                                   B. no                   Z                  P
                                                                   C. cannot be determined


                Since connecting the opposite vertices of a regular
                hexagon divides the hexagon into six congruent                                 S         T
                triangles, each central angle will be congruent. The
                measure of each angle is 360 ÷ 6 or 60.


                   Answer                   60                        Answer



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