25 Proving Angles Congruent

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2-5 Proving Angles Congruent
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Vertical Angles

• Angles formed
• by opposite rays.

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Adjacent Angles

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

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Complementary Angles

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

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Supplementary Angles

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

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Identify the Angles

• 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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Looking at a Diagram

• When looking at a diagram, we can conclude
• Vertical angles
• Adjacent angles
• Adjacent supplementary angles

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We cannot assume

• Angles or segments are congruent
• Angles are right angles
• Lines are parallel or perpendicular
• (unless there are marks that give this
  information)

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What can you conclude from the diagram?
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Find the value of x
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Find the value of x
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Congruent Complements Theorem

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

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Congruent Supplements Theorem

• 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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Congruent and Supplementary
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Find the value of both variables.
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Find the value of x.
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Find the measure of each angle.
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Find the measure of each angle.

• m?1
• m?2
• m?3
• m?4