Question
In fig 3.39 chord AB ≅ chord CD, Prove that, arc AC ≅ arc BD
✓
Answer
∵ chord AB ≅ chord CD
∴ m(arc AB) = m(arc CD){Corresponding arcs of congruent chords of a circle (or congruent circles) are congruent}
Subtract m(arc CB) from above,
m(arc AB)– m(arc CB) = m(arc CD) – m(arc CB)
⇒m(arc AC) = m(arc BD)
⇒arc AC ≅ arc BD
Hence, proved.
∴ m(arc AB) = m(arc CD){Corresponding arcs of congruent chords of a circle (or congruent circles) are congruent}
Subtract m(arc CB) from above,
m(arc AB)– m(arc CB) = m(arc CD) – m(arc CB)
⇒m(arc AC) = m(arc BD)
⇒arc AC ≅ arc BD
Hence, proved.
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