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107 Cards in this Set
- Front
- Back
Conjecture
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an unproven statement that is based on observations.
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Inductive Reasoning
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looking for patterns and making conjectures.
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Counterexample
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an example that shows a conjecture is false.
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Definition
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uses known words to describe a new word.
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Undefined Terms
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point, line, plane.
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Point
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has no dimension, and is represented by a small dot.
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Line
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extends in one dimension, represented by a straight line with arrowheads, and extends to infinity in both directions.
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Plane
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extends in two dimensions, is represented by a parallelogram, and extends to infinity, even though it appears to have edges.
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Collinear Points
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points that lie on the same line.
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Coplanar Points
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points that lie on the same plane.
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Segment
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a line that has a clear end and beginning.
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Ray
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a line that has one clear end and one that extends to infinity.
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Opposite Ray
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any pair of opposite rays forms a line--two rays that connect to each other.
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Intersect
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two or more geometric figures that have one or more points in common.
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Intersection
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the set of points the figures have in common.
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Postulate/Axioms
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rules that are accepted without proof.
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Theorem
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a rule that is proved.
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Coordinate
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a real number that corresponds to a point.
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Distance
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the absolute value of the difference between the coordinates.
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Between
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when three points lie on a line, you can say one is in "between" the other two.
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Distance Formula
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a formula for computing the distance between two points in a coordinate plane.
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Congruent Segments
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segments that have the same length.
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Angle
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consists of two different rays that have the same initial point.
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Sides
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the rays of the angle.
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Vertex
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the initial point of the angle.
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Congruent Angles
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angles that have the same measure.
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Interior
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the point of an angle if it is not on the angle or in its interior.
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How are angles classified?
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In categories according to their measures: acute, right, obtuse, and straight.
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Adjacent Angles
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two angles that share a common vertex and side, but have no common interior points.
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Midpoint
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the point that divides the segment into two congruent segments.
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Bisects
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divides.
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Segment Bisector
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a segment, ray, line, or plane that intersects a segment at its midpoint.
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Straightedge
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a ruler without marks.
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Construction
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a geometric drawing that uses a limited set of tools, usually a compass and a straightedge.
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Midpoint Formula
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taking the man, or average, of the x-coordinates and of the y-coordinates.
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Angle Bisector
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a ray that dives an angle into two adjacent angles that are congruent.
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Vertical Angles
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two angles that have sides from two pairs of opposite rays.
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Linear Pair
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two adjacent angles having non-common sides that are opposite rays--add up to 180 degrees.
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Complementary Angles
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two angles with the sum of their angles equaling 90 degrees--complementary to each other, can be adjacent or nonadjacent.
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Supplementary Angles
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two angles with the sum of their angles equaling 180 degrees--supplementary to each other, can be adjacent or nonadjacent.
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Conditional Statements
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two parts--hypothesis and a conclusion, written in if-then format.
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If-Then Format
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two parts--hypothesis and a conclusion, starts with "If..., then..."
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Converse
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formed by switching the hypothesis and conclusion.
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Negation
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writing the negative of the statement.
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Inverse
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negating the hypothesis and conclusion of a conditional statement.
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Contra-positive
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negating the hypothesis and conclusion of the converse of a condition statement.
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Perpendicular Lines
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intersecting to form a right angle.
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Line Perpendicular to a Plane
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a line that intersects the plane in a point and is perpendicular to every line in the plant that intersects it.
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Bi-conditional Statement
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a statement that contains the phrase "if and only if."
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Logical Argument
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facts, definitions, and accepted properties in a logical order.
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Law of Detachment
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If p -> q is true, and a conditional statement and p is true, then q is true.
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Law of Syllogism
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If p -> q and q -> r are true conditional statements, then p -> is true.
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Addition Prop(=)
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If a = b, then a + c = b + c.
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Subtraction Prop(=)
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If a = b, then a - c = b - c.
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Multiplication Prop(=)
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If a =b, then ac = bc.
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Division Prop(=)
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If a = b and c ≠ 0, then a ÷ c = b ÷ c.
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Reflexive Prop(=)
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For any real number a, a = a.
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Symmetric Prop(=)
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If a = b, then b = a.
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Transitive Prop(=)
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If a = b and b = c, then a = c.
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Substitution Prop(=)
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If a = b, then a can be substituted for b in any equation or expression.
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Reflexive Prop(=)
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For any segment AB, AB = AB.
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Symmetric Prop(=)
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If AB = CD, then CD = AB.
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Transitive Prop(=)
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If AB = CD and CD = EF, then AB = EF.
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Theorem
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a true statement that follows as a result of other true statements.
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Two-Column Proof
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a diagram with numbered statements and reasons that show the logical order of an argument.
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Paragraph Proof
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a proof written in paragraph form.
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Parallel Lines
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two lines that are coplanar and do not intersect.
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Skew Lines
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two lines that do not intersect and are not coplanar.
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Parallel Planes
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two planes that do not intersect.
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Transversal
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a line that intersects two or more coplanar lines at different points. It is classified by its sides and angles.
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Classification by Sides: Equilateral Triangle
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3 congruent sides.
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Classification by Sides: Isosceles Triangle
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At least 2 congruent sides.
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Classification by Sides: Scalene Triangle
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No congruent sides.
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Classification by Angles: Acute Triangle
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3 acute angles.
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Classification by Angles: Equiangular Triangle
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3 congruent angles.
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Classification by Angles: Right Triangle
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1 right angle.
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Classification by Angles: Obtuse Triangle
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1 obtuse angle
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Vertex
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each of the three points joining the sides of a triangle.
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Adjacent Sides
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two sides sharing a common vertex.
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Right Triangle: Legs
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the sides that form the right angle.
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Right Triangle: Hypotenuse
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the side opposite the right angle (in a right triangle).
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Isosceles Triangle: Legs
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When an isosceles triangle has only two congruent sides, then these two sides are LEGS of the isosceles triangle.
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Isosceles Triangle: Base
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The third side is the BASE of the isosceles triangle.
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Interior Angles
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the three original angles of a triangle.
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Exterior Angles
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The angles that are adjacent to the interior angles of a triangle.
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Corollary to a Theorem
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a statement that can be proved easily using the theorem.
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Congruent
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when two figures have a correspondence between their angles and sides so that the corresponding angles and corresponding sides.
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Corresponding Angles
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when the angles of a figure are all congruent.
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Corresponding Sides
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when the angles of a figure are all congruent.
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Base Angles
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the two angles adjacent to the base.
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Vertex Angle
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the angle opposite the base.
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Coordinate Proof
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involves placing geometric figures in a coordinate plane.
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Perpendicular Bisector
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a segment, ray, line, or plane that is perpendicular to a segment at its midpoint.
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Equidistant from Two Points
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a point that its distance from each point is the same.
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Distance from a point to a line
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the length of the perpendicular segment from the point to the line.
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Equidistant from the two lines
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when a point is the same distance from one line as it is from another line.
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Perpendicular Bisector of a Triangle
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a line (or ray/segment) that is perpendicular to a side of the triangle at the midpoint of the side.
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Concurrent Lines
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when three or more lines intersect in the same point.
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Point of Concurrency
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the point of intersection of the lines.
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Circumcenter of the Triangle
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the point of concurrency of the perpendicular bisectors of a triangle.
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Angle Bisector of a Triangle
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a bisector of an angle of the triangle.
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Incenter of the Triangle
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the point of concurrency of the angle bisectors.
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Median of a Triangle
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a segment whose endpoints are a vertex of the triangle and the midpoint of the poopsite side.
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Centroid of the Triangle
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the three medians of a triangle are concurrent; the point of concurrency is called the CENTROID.
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Altitude of a Triangle
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the perpendicular segment from a vertex to the opposite or to the line that contains the opposite side.
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Orthocenter of the Triangle
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the lines containing the altitudes are concurrent and intersect at a point.
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Mid-segment of a Triangle
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a segment that connects the midpoints of two sides of a triangle.
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