GEOMETRY NOTES

Chapter 1 : Points, Lines, and Planes

Review of Algebra Use number patterns and geometric patterns to practice making CONJECTURES. Conjectures can NOT be proved by showing specific examples in which the conjecture is true, but a conjecture can be disproved by finding ONE Counter-example. UNDEFINED TERMS: POINT: A location in space or on a plane, dimensionless LINE: Straight, no thickness, goes on forever in both directions       Parts of a Line:  Ray ,   Line Segment PLANE: Imaginary flat surface goes on forever in all directions. Lines can be Parallel, Intersecting, or Skew Intersecting lines are coplanar. Planes can be parallel or intersecting.  2 intersecting planes will intersect in a line. POSTULATE: Statement accepted as true without proof. Segment Additon Postulate: If A, B, and C are collinear and B is BETWEEN A and C, then AB + BC = AC DEFINITIONS: For point B to be BETWEEN points A and C, it must be collinear with A and C.

Distance Formula

The DISTANCE FORMULA is a form of the PYTHAGOREAN THEOREM.

Midpoint Formula

The MIDPOINT of a line segment  AB is the point "M"  if M is between A and B so that AM = MB

ANGLE classifications ACUTE, RIGHT, OBTUSE, STRAIGHT, REFLEX

ANGLE BISECTOR QR bisects <PQS only if <PQR = <RQS

Angle Addition Postulate: If R is in the interior or <PQS  then m<PQR + m<RQS = m<PQS

ANGLE PAIRS Complementary: 2 angles whose sum is 90 Supplementary: 2 angles whose sum is 180 Linear Pair: Supplementary Adjacent Angles Vertical Angles: Non-adjacent angles formed by 2 intersecting lines

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