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Essential Geometry Concepts: Definitions, Postulates, and Properties

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This review covers fundamental geometry concepts, including definitions and postulates essential for understanding relationships in geometry. Key topics include the Segment Addition Postulate, Angle Addition Postulate, the Definition of Congruence, and classifications of angles (acute, obtuse, right, and straight). It also discusses critical postulates such as the Linear Pair Postulate, the Vertical Angles Theorem, and the Congruent Supplements and Complements Theorems. Mastering these concepts will solidify your foundation in geometry and enhance problem-solving skills.

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Essential Geometry Concepts: Definitions, Postulates, and Properties

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Presentation Transcript

  1. HEY REMEMBER ME!!!!!! DEFINITIONS, POSTULATES, AND PROPERTIES Review

  2. SEGMENT ADDITION POSTULATE If B is between A and C then AB + BC = AC

  3. ANGLE ADDITION POSTULATE If B is in the interior of ACD then: m ACB + m BCD = m ACD

  4. DEFINITION OF CONGRUENCE Ifthen AB = CD

  5. DEFINITION OF AN ACUTE ANGLE Angle whose measure is between 0 and 90 degrees

  6. DEFINITION OF AN OBTUSE ANGLE Angle whose measure is between 90 and 180 degrees

  7. DEFINITION OF A RIGHT ANGLE Angle whose measure is 90 degrees

  8. DEFINITION OF A STRAIGHT ANGLE Angle whose measure is 180 degrees

  9. DEFINITION OF A MIDPOINT Point that divides a segment into two congruent parts

  10. DEFINITION OF ANANGLE BISECTOR Ray that divides an angle into two congruent adjacent angles

  11. DEFINITION OF COMPLEMENTARY ANGLES 2 angles whose sum is 90

  12. DEFINITION OF SUPPLEMENTARY ANGLES 2 angles whose sum is 180

  13. DEFINITION OF PERPENDICULAR LINES If 2 lines are perpendicular then they form RIGHT angles.

  14. LINEAR PAIR POSTULATE If two angles form a linear pair, then they are supplementary.

  15. VERTICAL ANGLES THEOREM Vertical angles are congruent.

  16. NEW THEOREMS & POSTULATES

  17. RIGHT ANGLE CONGRUENCETHEOREM All right angles are congruent

  18. Congruent supplements theorem If two angles are supplementary to the same angle (or to congruent angles) then they are congruent.

  19. CONGRUENT COMPLEMENTS THEOREM If two angles are complementary to the same angle (or to congruent angles) then they are congruent.

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