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2.6 Deductive Reasoning

2.6 Deductive Reasoning. GEOMETRY. Special Pairs of Angles. Vertical angles Linear pair of angles Complementary angles Supplementary angles. Vertical Angles. Definition: If two angles have their sides that form two pairs of opposite rays, then the two angles are vertical angles.

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2.6 Deductive Reasoning

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  1. 2.6 Deductive Reasoning GEOMETRY

  2. Special Pairs of Angles • Vertical angles • Linear pair of angles • Complementary angles • Supplementary angles

  3. Vertical Angles Definition: If two angles have their sides that form two pairs of opposite rays, then the two angles are vertical angles. VERTICAL ANGLES THEOREM: If two angles are vertical angles, then they are congruent.

  4. Linear Pair Definition: If two angles are adjacent and their noncommon Sides are opposite rays, then the two angles form a linear pair. • LINEAR PAIR POSTULATE: • If two angles for a linear pair, then • They are supplementary • The sum of their measures is 180o.

  5. Complementary Angles Definition: If two angles have a sum of 90o, then the two angles are complementary angles. Each angle is the complement of the other. The angles themselves do not have to be adjacent, but if they are, they must form a “perfect” corner.

  6. Congruent Complements Theorem If two angles are complementary to the same or to congruent angles, Then the two angles are congruent. If A and B are complementary andC and B are complementary then A  C because both A and C are complementary to B.

  7. Supplementary Angles Definition: If two angles have a sum of 180o, then the two angles are complementary angles. Each angle is the supplement of the other. The angles themselves do not have to be adjacent, but if they are, they must form a straight line.

  8. Congruent Supplements Theorem If two angles are supplementary to the same or to congruent angles, Then the two angles are congruent. If A and B are supplementary andC and B are supplementary then A  C because both A and C are supplementary to B.

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