Geometry Vocab Ch. 3-5 – Flashcards
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Equidistant
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the distance between two lines measured along a perpendicular line is always the same
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Parallel lines
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coplanar lines that don't intersect
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point slope form
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y-y1=m(x-x1)
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Rate of change
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describes how a quantity is changing over time
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skew lines
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lines that don't intersect and aren't coplanar
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slope
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m in m=y2-y1/ x2x1
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slope intercept form
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a linear equation in y=mx+b
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transversal
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a line that intersects two or more coplanar lines at two different points.
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acute angle
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angle less than 90 degrees
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auxiliary line
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extra line or segment drawn in a figure to help complete a proof
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base angles
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the 2 angles formed by the base and the congruent sides
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congruence transformations
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a mapping for which a geometric figure and its image are congruent
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congruent polygons
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polygons in which all matching parts are congruent
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coordinate proofs
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proofs that use figures in the coordinate plane and algebra to prove geometric concepts
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corollary (of a theorem)
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a statement that can be easily proved using a theorem
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corresponding parts
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matching parts of congruent polygons
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equiangular triangle
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a triangle with all angles congruent
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equilateral triangle
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a triangle with all sides congruent
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exterior angle
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angles formed by one side of a triangle and the extension of another side
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flow proof
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a proof that organizes statement in a logical order- at is written in a box with its reason under the box and arrows indicate the order of the statements
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included angle
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in a triangle, the angle formed by two sides
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included side
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the side of a polygon that is a side of each of two angles
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isosceles triangle
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a triangle with at least two sides congruent sides called legs
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obtuse triangle
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a triangle with an obtuse angle (more than 90)
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reflection
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a tranformation representing the flip of a figure over a point, line, or plane
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remote interior angles
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the angles of a triangle that aren't adjacent to a given exterior angles; the ones farthest away from the exterior angle/ the one that is extended
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right angle
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an angle that measure 90
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rotation
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a transformation that turns every point of a premiere that a specified angle and direction about a fixed point- the center of rotation.
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scalene triangle
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a triangle with no 2 sides congruent/ all the sides are different
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translation
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a transformation that moves a figure the same distance in the same direction.
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vertex angle
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angle with sides that are the legs (of an isosceles triangle)
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altitude
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in a triangle, a segment from a vertex of the triangle to the line contain the opposite side and perpendicular to that side
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centroid
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the point of concurrency of the medians of a triangle
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circumcenter
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the point of concurrency of the perpendicular bisector of a triangle
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concurrent lines
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3 or more lines that intersect at a common point
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indirect proof
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one assumes that the statement to be proved is false. You use logical reasoning to deduce that a statement contradicts a postulate, theorem, or one of the assumptions. Once this is made, one concludes that the statement assumed false must be true.
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indirect reasoning
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assumes that the conclusion is false and then shows that this assumption leads to a contradiction of the hypothesis like a postulate, theorem, or corollary. Then, since it has been proved false, the conclusion must be true.
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median
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in a triangle, a line segment with endpoints that are a vertex of the triangle and the midpoint of the side opposite the vertex
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orthocenter
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the point of concurrency of the altitudes of a triangle
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perpendicular bisector
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in a triangle, a line, segment, or ray that passes through the midpoint of a side and is perpendicular to that side
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point of concurrency
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the point of intersection of concurrent lines
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proof by contradiction
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an indirect proof in which one assumes that the statement to be proved is false. one then uses logical reasoning to deduce a state,went that contradicts a postulate, theorem, or one of the assumptions. Once this is obtained, one concludes that the statement assumed false must in fact be true.
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supplementary angles
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two angles that add up to 180
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alternate interior angles
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two angles on opposite sides of the transversal but inside the parallel lines
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alternate exterior angles
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two angles on opposite sides of the transversal but outside the parallel lines
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corresponding angles
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two angles on the same side of the transversal- both above or below the lines
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consecutive interior angles
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two angles that lie on the same side of the transversal inside of the lines
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complementary angles
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two angles that add up to 90
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postulate
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accepted as true without proof
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theorem
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Can be proven true by undefined terms, definitions, and postulates.
