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Transcript
Vocabulary Definitions Unit 1 Point: Indicates a location and has no size. You will name a point by using a capital letter. Point A Line: Extends in two opposite directions without ending. It has no thickness. A line contains an infinite number of points. We name a line with two points on the line or by a single lowercase letter. β‘ Line π or π΄π΅ Plane: is a flat surface that extends without end and has no thickness. A plane contains an infinite number of lines. A plane is name by a capital letter or by at least 3 points within in the plane that are NOT on the same line. Plane P or Plane ABC Space: the set of all points. Collinear points: points that lie on the same line. Points D, E and F are collinear. Coplanar points: points that lie in the same plane. (You can also have other coplanar figures) Points A, B and C are coplanar in Plane P. Segment: a part of a line that consists of two endpoints and all the points in between them. You name a segment by its two endpoints. Μ Μ Μ Μ or π΅π΄ Μ Μ Μ Μ Segment π΄π΅ Ray: is part of the line that consists of only one endpoint and all the points on one side of the line. You name a ray by its endpoint and one point on the ray. The order of the points indicates the rayβs direction. Ray π΄π΅ Opposite Rays: Two rays that share the same endpoint and form a line. πΈπ· πππ πΈπΉ are opposite rays. Congruent Segments: segments that have equal measure. Midpoint of a Segment: The point on a segment that divides it into two congruent segments. Segment Bisector: The ray, segment, line or plane that intersects a segment at its midpoint. Segment Addition Postulate: If points A, B and C are collinear and B is between A and C, then AB + BC = AC. Ratio: A comparison of two quantities using division. Partition: to divide into equal parts. Angle: formed by two rays with a common endpoint. The rays are the sides of the angle and the vertex is the common endpoint. β π΅π΄πΆ, β πΆπ΄π΅,β π΄ or β 1 Acute Angle: an angle whose measure is between 0 and 90 degrees. Right Angle: an angle whose measure is exactly 90 degrees. Obtuse Angle: an angle whose measure is between 90 and 180 degrees. Straight Angle: an angle whose measure is exactly 180 degrees. Adjacent Angle: two angles is a plane that have a common vertex and common side but no common interior points. Linear Pair: A pair of angles who non-common sides are opposite rays. They form a straight angle, so therefore, they are supplementary. Angle Addition Postulate: The measure of the smaller angles will sum to the whole angle. πβ π΄ππ΅ + πβ π΅ππΆ = πβ π΄ππΆ. Vertical Angles: two angles whose sides form opposite rays. Their measures are congruent. Complementary Angles: two angles whose measures sum to 90 degrees. Supplementary Angles: two angles whose measures sum to 180 degrees. Angle Bisector: a ray that divides an angle into two congruent angles. Congruent Angles: angles that have the same measure Conditional: an if-then statement. It has 2 parts, they hypothesis which comes after the if and the conclusion which is after the then. βIf p, then q.β Converse: switch the hypothesis and conclusion of the conditional statement. βIf q, then p.β Inverse: Negate the conditional statement. βif not p, then not q.β Contrapositive: Negate the converse statement. βIf not q, then not p.β Truth Value: determines if a conditional is true or false. Hypothesis true and conlusion trueβ¦β¦β¦β¦β¦.statement is true. Hypothesis true and conclusion falseβ¦β¦β¦β¦.statement is false. Counterexample: an example that proves a statement false. Parallel Lines: coplanar lines that never intersect. a ll b Perpendicular Lines: coplanar lines that intersect and form a right angle. Skew Lines: noncoplanar lines that never intersect and are not parallel. β‘ and π·πΈ β‘ are skew. π΄π΅ Parallel Planes: two planes that never intersect. Perpendicular Planes: two planes that intersect at a right angle. Transversal: a coplanar line that intersects two or more lines. Corresponding Angles: angles that lie in the same position (corresponding position) relative to the transversal. Corresponding angles are congruent, IF lines are parallel. Alternate Interior Angles: nonadjacent interior angles that are on opposite sides of the transversal. Alternate interior angles are congruent, IF lines are parallel. Alternate Exterior Angles: nonadjacent exterior angles that are on opposite sides of the transversal. Alternate Exterior angle are congruent, IF lines are parallel. Same-Side Interior Angles: Interior angles on the same side of the transversal. Same-Side interior angles are supplementary, IF lines are parallel.