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Transcript
TLQP Geometric Concepts and Definitions Mathematical System: Undefined Terms, axioms, definitions, theorems Euclid (300 BCE) Geometry undefined terms points P, Q, R, A, B, “no size” AB , straight, collinear Line Segment AB , midpoint, bisect lines planes flat, half-planes Ray (half-line) AB Line A line segment consists of two points on a line and all the points between them. The line segment with endpoints A and B is denoted by AB . A point on a line partitions the line into three disjoint sets: the point and two half-lines. A ray consists of a point on a line and all the points in one of the half-lines determined by the point. Angle Measurements An angle is formed by the union of two rays, with a common endpoint. This endpoint is called the vertex, and the rays are called the sides of the angle. Degrees, minutes, seconds 360 - one full revolution “Acute angle” < 90 = “right angle” < “obtuse angle” < 180 = “straight angle” < “reflex angle” Complementary angles sum to 90 Supplementary angles sum to 180 Adjacent angles share a common side. An exterior angle of a polygon is formed by the extension of one side thought a vertex of the polygon and the other side of the polygon through that vertex. Perpendicular lines meet to form right angles Parallel lines are lines in a plane that do not meet. Two lines are parallel if and only if alternate interior angles are equal. 1 2 A circle is the set of all points in a plane that are equidistant from a fixed The radius is a line segment from appoint on the circle to the center. A chord is a line segment whose endpoints are both on the circle. A diameter is a chord that passes through the center. A tangent is a line that intersects the circle is exactly one point. The circumference is the distance around the circle. A disk is the union of a circle and its interior. point, called the center. chord diameter radius tangent