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Mathematics, 19.07.2021 18:10 alicciardone01
Proving That Congruent Central Angles Have Congruent Chords
Given: ⊙O with central angles ∠AOC ≅ ∠BOD
Prove: AC ≅ BD
Circle O is shown. Line segments O A, O C, O B, and O D are radii. Line segments connect points A and C and points B and D to form 2 triangles inside of the circle. Angles A O C and B O D are congruent.
Complete the missing parts of the paragraph proof.
Proof:
We know that central angles
are congruent, because it is given. We can say that segments AO, CO, BO, and DO are congruent because
. Then by the
congruency theorem, we know that triangle AOC is congruent to triangle BOD. Finally, we can conclude that chord AC is congruent to chord BD because
.
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Proving That Congruent Central Angles Have Congruent Chords
Given: ⊙O with central angles ∠AOC ≅ ∠B...
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