Given:
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Two points determine a line.
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because alternate interior angles of parallel lines cut by a transversal are congruent.
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?
because of
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?
because
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Given: ? |
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? Two points determine a line. |
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? because alternate interior angles of parallel lines cut by a transversal are congruent. |
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? |
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? because of ? |
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? because ? |
Circle A with parallel
chords BC and ED
Draw segment EC
m ∠ E ≅ m ∠ C
m ∠ C =
1 over 2
1
2
m 
EB m ∠ E ≅
1 over 2
1
2
m CD
because the measures of inscribed angles are half
their intercepted arcs
1 over 2
1
2
m CD
=
1 over 2
1
2
m EB
substitution
the multiplicative
property of equality
m CD
=
m EB
∴
CD
≅
EB
congruent arcs
have equal measures