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95 Cards in this Set

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 the distance postulate to every pair of different points there corresponds a unique positive number The Ruler Postulate To every point of the line corresponds exactly one real number, to every real number corresponds exactly one point on the line, and the distance between any two points is the absolute value of the difference of the corresponding numbers The Ruler Placement Postulate Given two points P and Q on a line, P is zero and the coordinate of Q is positive The Line Postulate For every two points there is exactly one line that contains both points Every plane contains (points) at least three noncollinear points Space contains (points) at least four noncollinear points IF two points on a line lie in a plane, the the line lies in the same plane. The Plane Postulate Any three points lie in at least one plane, and any three noncollinear points lie in exactly one plane. If two plane intersect their intersection is a line To every angle there corresponds a number between 0-180 Angle Addition Postulate Self-explanatory The Supplement Postulate If two angles form a linear pair, they they are supplementary The SAS postulate SAS congruence ASA postulate ASA congruence SSS postulate SSS congruence the Parallel postulate through a given external point there is only one parallel to a given line The Area Postulate To every polygonal region there corresponds a unique positive real number The Congruence Postulate If two triangles are congruent then their triangular regions have the same area. The Area Addition Postulate If two polygonal regions intersect only in edges and vertices (or do not intersect at all) then their area is the union of the sum of their areas. The Unit Postulate The area of a square region is the square of the length of its edges The are of a rectangle is the product of the altitude and the area of the base If A B and C are three different points of the same line then exactly one of them is in between the other two Given a line and a point not on the line there is exactly one plane containing both. Given two intersecting lines there is exactly one plane containing it. If two angles are complementary then they are acute angles If two angle are congruent and supplementary then each is a right angle The Supplement Theorem supplements of congruent angles are congruent The Complement Theorem Complements of congruent angles are congruent The Vertical Angle Theorem Vertical angles are congruent If two intersecting lines form one right angle then they form four right angles The Angle Bisector Theorem Every angle has exactly one bisector The Isosceles Triangle theorem If two sides of a triangle are congruent then the angles opposite them are congruent. Converse Isosceles Triangle Theorem If two angles of a triangle are congruent then the sides opposite them are congruent The Perpendicular Bisector Theorem The perpendicular bisector of a segment in a plane is the set of all points of the plane that are equidistant from the end points of the segment Parts theorem the part is smaller than the whole The Exterior angle theorem exterior is greater than remote. In fact, exterior is the sum of the two remote. the SAA theorem SAA congruence Hypotenuse leg Theorem if the hypotenuse and one leg is congruent and it's a right triangle, they're congruent Longer side angle theorem Longer side is opp of larger side and smaller side smaller angle, if it's the same triangle. If two angles of a triangle are not congruent then the sides are not congruent The first minimum theorem the shortest segment is the perpendicular segment the triangle inequality the sum of the length of any two sides is greater than the length of the third side. the Hinge theorem If two sides of one triangle are congruent to two sides of another and the included angle of the first is larger, than the included angle of the second, then the side to the first one is longer to the other one. Converse Hinge theorem converse of hinge. but it's longer segment to angle instead of opposite. Triangle Inequality the sum of the length of any two sides of a triangle is greater than the length of the third side. If B and C are equidistant from P and Q then every point between B and C is equidistant from P and Q if a line and a plane are perpendicular then the plane contains every line perpendicular to the given point at its intersection with the given plane the perpendicular bisecting plane theorem the perpendicular bisecting plane of a segment is the set of all points equidistant from the end points of the segment second minimum theorem the shortest segment to a plane from an external point is the perpendicular segment two parallel lines lie in exactly one plane alternate interior congruent corresponding angles congruent same side interior supplementary if two lines are parallel to same line, then they are parallel to each other the sum of the measures of a triangle is 180 in a parallelogram opposite sides are congruent and consecutive angles are supplementary. the diagonal of a parallelogram bisects each other in a quad., the two opp sides are congruent it is a parallelogram in a quad if a pair of sides are both parallel and congruent its a parllelogram if diagonals of a quad bisect each other it's a parallelogram in a rhombus the diagonals are perpendicular to each other midsegment theorem midsegment is half and parallel to third side in a quadrilateral if one right angle then four right angle if the diagonals of a quadrilateral bisect each other and are perpendicular then the quad is a rhombus. the median to the hypotenuse of a right triangle is half as long as the hypotenuse 30-60-90 1, 2, square root of three if one leg of a right triangle is half as long as the hypotenuse the opposite angle has measure of 30 parallel lines are always equidistant area of trapezoid is half the bases x altitude if two triangles ahve the same bases and altitudes they have the same area if two triangles ahve the same altitude h, then the ratio of their areas is the ratio of their bases the pythag thereom a^2 + b^2=C^2 converse pythag theroem if using pythag theorem it fits, then it's a right triangle the isosceles right triangle theorem 45-45-90 is 1-1-square root of 2 the basic proportionality theorem if a line is parallel to one side of the triangle it creates similar triangles if a line intersects and makes proportional segments then it is parallel to third side AA similarity theorem triangles with this are similar SAS similarity triangles with this are similar SSS similarity triangles with this are similar given a right triangle and the altitude of the hypotenuse the altitude is the geometry mean of the segments into which it separates the hypotenuse Each leg is the geometry mean of the hypotenuse and the segment of the hypotenuse adjacent to the leg If two triangles are similar then the ratio of their areas is the square ratio of any two corresponding sides a line perpendicular to a radius at its outer end is tangent to the circle every tangent to a circle is perpendicular to the radius drawn to the point of contact the perpendicular from the center of a circle to a chord bisects the chord the segment from the center of a circle to the midpoint of a chord which is not a diameter is perpendicular to the chrod the perpendicular bisector of a chord passes through the center in the same circle or in congruent circle any two congruent chords are equidistant from the center the line-circle theorem if a line and circle are coplanar and the line intersects the interior of a circle then it intersects the circle in two and only two points a plane perpendicular to the radius at the outer end is tangent to the sphere the arc addition theorem you can add arcs the inscribed angle theorem the measure of an inscribed angle is half the measure of tis intercepted arc in the same circle or in congruent circles, if two arcs are congruent so are the corresponding chords The tangent-secant theorem given an angle with its vertex on a circle, formed by a secant ray and a tangent ra, the measure of the angle is half the measure fo the intercepted arc. the two-tangent if two tangent segments to a circle from a point of the exterior are congruent and determine congruent angles with the segment from the exterior point to the circle the median concurrence theorem medians of triangles when intercepted is two thirds the way if two arcs have equal radii then their lengths are proportional to their measuers