Standard 2.0, 4.0.  Angles formed by opposite rays.

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Presentation transcript:

Standard 2.0, 4.0

 Angles formed by opposite rays.

 Angles that share a common side and a common vertex, but have no common interior points.

 Two angle whose measures have a sum of 90 degrees.  or

 Two angles whose measures have a sum of 180 degrees.  or

Name a pair of vertical angles. Name a pair of adjacent Angles. Name a pair of complementary angles. Name a pair of supplementary angles.

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!

If two angles are complementary to the same angle (or congruent angles), then the two angles are congruent.

If two angles are supplementary to the same angle (or congruent angles), then the two angles are congruent.

All right angles are congruent.

m∠1m∠2m∠3m∠4m∠1m∠2m∠3m∠4

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