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Published byRalph Nelson Modified over 9 years ago
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Standard 2.0, 4.0
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Angles formed by opposite rays.
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Angles that share a common side and a common vertex, but have no common interior points.
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Two angle whose measures have a sum of 90 degrees. or
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Two angles whose measures have a sum of 180 degrees. or
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Name a pair of vertical angles. Name a pair of adjacent Angles. Name a pair of complementary angles. Name a pair of supplementary angles.
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Prove that EVERY pair of vertical angles is congruent by proving that 2 4. StatementReason Angles 1, 2, 3, and 4 created by intersecting lines Given Angle 2 and 4 are vertical.Definition of vertical angles. Angle 2 and 3 make a straight angle. Angle 3 and 4 make a straight angle. Definition of straight angle. m 2 + m 3 = 180 m 3 + m 4 = 180 Angle Addition Postulate m 2 + m 3 = m 3 + m 4 Substitution m 2 = m 4 Subtraction property of Equality QED Theorem 2.1: All vertical angles are congruent!
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If two angles are complementary to the same angle (or congruent angles), then the two angles are congruent.
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If two angles are supplementary to the same angle (or congruent angles), then the two angles are congruent.
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All right angles are congruent.
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m∠1m∠2m∠3m∠4m∠1m∠2m∠3m∠4
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Page 112-113 #1-3, 10, 12-18 & 30-32
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