Math 150

Fundamental Theorems

Dr. Wilson

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1.1 Two points determine a straight line.

1.2 Two lines are either parallel or they meet at a single point.

1.3 Given a line and a point not on the line, there is a uniquely determined line through the point parallel to the given line.

1.4 Given a line and a point, there is a uniquely determined line through the point perpendicular to the given line.

1.5 A line is parallel to one of two parallel lines if and only if it is parallel to the other.

1.6 If a line is perpendicular to one of two parallel lines, then it is perpendicular to the other

1.7 If two lines are both perpendicular to the same line, they are parallel to each other.

1.8 Vertical angles are the same size

1.9 if two lines are crossed by a transverse line, the following conditions are equivalent

  1. the lines are parallel
  2. the alternate interior angles are the same size
  3. the opposite interior angles are supplementary
  4. the corresponding angles are the same size

1.9 The angles in a triangle add up to 180o.

1.10 The congruent triangle cirteria

  1. SSS
  2. SAS
  3. ASA
  4. AAS
  5. HS

The last criterion, HS, Hypoteneuse Side follows from the fact that if you know two sides in a right triangle, you can use the Pythagorean Theorem to find the third side, and then you can use SSS.