Page 160 - Math Course 3 (Book 2)
P. 160

Circles: Arcs and Chords
          Mo. 11


           Lesson 3                                         THEOREM 11.2



                                                            In a circle or in congruent circles, two minor arcs
                                                            are congruent if and only if their corresponding
          KEY CONCEPTS:
                                                            chords are congruent.
          1. Recognize and use relationships between
              arcs and chords.                              Abbreviation:
          2. Recognize and use relationships between        In ⊙, 2 minor arcs are ≅, corr. chords are ≅.
              chords and diameters.                         In ⊙, 2 chords are ≅, corr. minor arcs are ≅.

                                                            Examples:
                                                                                   A
                                                            If AB ≅ CD, AB ≅ CD.
          MO. 11 - L3a                                                                               B
                                                            If AB ≅ CD, AB ≅ CD.
             The Relationships Between
                    Arcs and Chords                                                                  C
                                                                                 D


                     Vocabulary A-Z
                     Let us learn some vocabulary


                                                                         Let’s Begin
         inscribed
         A polygon is inscribed if all of its vertices lie on the
         circle.
                                                           Prove Theorem 11.2
            Quadrilateral ABCD is an inscribed polygon
             because all of its vertices lie on the circle.   Example
                             A



                                                            Proof:  Write a two-column proof.
                    D             E       B
                                                            Given:  DE ≅ FG
                                                                   m∠EBF = 24

                             C                                     DFG is a semicircle.

         circumscribed                                      Prove:  m∠FBG = 78
         a circle is circumscribed about a polygon if it
         contains all the vertices of the polygon.                                       G

            Circle E is circumscribed about the polygon                F
         because it contains all the vertices of the polygon.
                             A                                    E


                                                                                   B
                    D             E       B



                                                                         D
                             C
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