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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 ?135
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Name a pair of vertical angles.
Name a pair of adjacentAngles.
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.
Statement ReasonAngles 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.
m2 + m3 = 180 m3 + m 4 = 180
Angle Addition Postulate
m2 + m3 = m3 + m 4 Substitution
m2 = 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∠1
m∠2
m∠3
m∠4
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Homework
Page 112-113#1-3, 10, 12-18 & 30-32