direct reasoning, direct proof: information that is known to be true
indirect reasoning, indirect proof: When all possibilities are rules out but one thought to be true.
contradictory, contradiction: When two statements cannot be true at the same time.
Law of Indirect Reasoning: If statement p leads to a false conclusion, then p is false.
tangent: A line which intersects a circle at exactly one point.
point of tangency: The point of intersection between a tangent and the circle.
Radius-Tangent Theorem: A line is tangent to a circle if and only if it is perpendicular to a radius at the radius's endpoint on the circle.
common tangents: When two different circles share the same tangents.
uniquely determined: When there is only one of them and no way for another.
auxiliary: Something uniquely determined to a figure.
Uniqueness of Parallels Theorem: Through a point not on a line, there is exactly one parallel to the given line.
Postulates of Euclid:
1. Two points determine a line segment.
2. A line segment can be extended indefinitely along a line.
3. A circle can be drawn with any center and any radius.
4. All right angles are congruent.
5. If two lines are cut by a transversal, and the interior angles on the same side of the transversal have a total measure of less than 180, then the lines will intersect on that side of the transversal.
non-Euclidian: Types of Geometry for other surfaces.
exterior angle: An angle that forms a linear pair with any other angle in a polygon.
Exterior Angle Theorem: In a triangle, the measure of an exterior angle is equal to the sum of measure of the two nonadjacent interior angles.
Exterior Angle Inequality: In a triangle, the measure of an exterior angle is greater than the measure of either nonadjacent interior angle.
Unequal Sides Theorem: If two sides of a triangle are not congruent, then the angles opposite them are not congruent, and the larger angle is opposite the larger side.
Unequal Angles Theorem: If two angles of a triangle are not congruent, then the sides opposite them are congruent, and the longer side is opposite the larger angle.
Exterior Angles of a Polygon Sum Theorem: In any convex polygon, the sum of the measures if the exterior angles, one at each vertex, is 360.
Homework Help: Math: Arithmetic
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