1 / 8

Exploring Special Angle Relationships in Geometry

Gain insights into the concepts of vertical angles, linear pairs, complementary, and supplementary angles in geometry through deductive reasoning principles.

walterbland
Download Presentation

Exploring Special Angle Relationships in Geometry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related