MBI_THE PROOF FINDER: Chord Arc Theorem
Chord Arc Theorem
If two chords in a circle are congruent, then their intercepted arcs are congruent.
DIRECTIONS:
This proving activity is a sort of game. If you got a perfect score, you will earn the MBI Agent Badge. MBI stands for Math Bureau of Investigation. It is related to investigation because every statement must be provided with accurate reason in order to prove the theorem correctly.
Given the circle below, point O is the center and line segment FG and line segment BY are chords, and they are congruent (≅).Prove that arc FG ≅ arc BY.
Statement 1: Point O is the center
Reason
Statement 2: Draw line segment OF, line segment OG, line segment OB and line segment OY.
Reason 2
Statement 3: Line segment OF, line segment OG, line segment OB and line segment OY are radii.
Reason 3
Statement 4: Line segment OF is congruent to line segment OG.
Reason 4
Statement 5: Line segment OG is congruent to line segment OY.
Reason 5
Statement 6: Line segment FG is congruent to line segment BY.
Reason 6
Statement 7:△ FOG ≅ △ BOY
Reason 7
Statement 8: ∠ FOG ≅ ∠ BOY
Reason 8
Statement 9: ∠ FOG and ∠ BOY are central ∠s.
Reason 9
Statement 10: m∠ FOG = measure arc FG ,and m∠ BOY = measure arc BY.
Reason 10
Statement 11. arc FG ≅ arc BY
Reason 11
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