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17 Cards in this Set
- Front
- Back
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Define parallel lines
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Two distinct lines are parallel if they are contained in the same plane and have no point in common (no point of intersection)
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Define collinear points
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Three or more points are collinear if they are on the same line.
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Name Euclid's five postulates
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1. A straight line can be drawn between any two points.
2. Any straight line segment can be extended indefinitely to form a straight line. 3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center. 4. All right angles are congruent. 5. If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. |
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What is the definition of a Euclidean Geometry?
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Euclidean geometry is an incidence geometry that satisfies this parallel axiom:
If we consider line L and any point P where P is not on L, then there exists exactly one line on P that is parallel to L. This axiom is also called the Euclidean postulate. |
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Define: Concurrent Lines
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Three or more lines are called concurrent if they pass through the same point.
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Define: Line Segment
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Line segment AB is the set of all points X on the line AB whose coordinates are in-between the coordinates X[a] and X[b] of A and B.
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Define: Ray
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The ray AB is the set of points on the line AB whose coordinates X are in the same order relation to X[a] as X[b] is to X[a]. The point A is called the endpoint of the ray.
From the web: A part of a line starting at a particular point and extending indefinitely in one direction. |
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Define: Polygonal Line
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A union of three or more line segments, called sides, at distinct points in the plane, called vertices.
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Define: Polygon
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A polygonal line in which two consecutive sides intersect only at a vertex and all non-consecutive sides do not intersect.
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Define: Regular Polygon
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A polygon in which all sides have the same measure and all angles have the same angular measure. (All sides are congruent and all angles are congruent).
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Define: Convex Regions
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A set of points in the plane (region) is called convex if for any two points A and B in the region, the line segment AB is contained within the region.
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Define: Angle
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The union of two rays joined at a common endpoint, called the vertex. The rays are called sides.
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Define: Straight Angle
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An angle AOB whose sides OA and OB form the line AB (an angle whose sides form a line).
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Define: Interior of an angle
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The convex region formed by an angle that is not a straight angle.
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Define: Adjacent angles
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Two angles which share a common vertex and a common side and have disjoint interiors.
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Define: Right Angle
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Half of a straight angle.
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Define: Angle Measurement
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A number between 0 and 180 degrees or 0 and pi radians that denotes the amount of rotation about the vertex that occurs between the two rays that form the sides of an angle.
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