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### 87 Cards in this Set

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 If a point is on the perpendicular bisector of a segment then the point is equidistant from both endpoints of the segment If a point is equidistant from both endpoints on segment then it is on the perpendicular bisector If a point is on the bisector of and angle then it is equidistant from the two sides of the angle The Perpendicular bisector s of a triangle intersect at a point that is equidistant from the vertices of the triangle The angle bisectors of a triangle intersect at a point that is equidistant form the sides of the triangle. The Medians of a triangle intersect at a point that is two thirds of the distance from each vertex to the midpoint of the opposite side The lines containing the altitudes of a triangle are congruent The segment connecting the midpoints of two sides of a triangle is parallel to the third side and half as long. If one side of a triangle is longer than another side then the angle opposite of the longer side is larger than the angle opposite the shorter side If one angle is larger than another angle the segment opposite the larger angle is larger than the segment opposite the smaller angle. The measure of an exterior angle of a triangle is greater than the measure of the two nonadjacent interior angles The Sum of the lengths of any two sides of a triangle is greater than the length of the third side If two sides of one triangle are congruent to two sides of another triangle and the included angle of the second and the third side of the first is longer than the third side of the second If two sides of one triangle are congruent to two sides of another triangle and the third side of the first is longer than the third of the second then the included angle of the first is larger than the included angle of the second Polygon is a plane figure that meets the following conditions It is formed by three or more segments called sides Each sides intersects with exactly two other sides Each endpoint in a polygon is a Vertex Equilateral means all sides are Congruent Equiangular means all angles are Congruent Regular means that a polygon is both equilateral and equiangular Parallelograms are quadrilaterals that have 2 pairs of parallel sides Parallelograms opposite sides are Congruent Parallelograms opposite angles are Congruent Parallelograms consecutive angles are supplementary Parallelograms diagonals bisect each other Rhombuses are Parallelograms with 4 congruent sides Rectangles are Parallelograms with 4 right angles Squares are are Parallelograms with4 congruent sides and 4 right angles A Parallelogram is a rhombus if and only if it’s diagonals are perpendicular A Parallelogram is a rhombus if and only if if each diagonal bisects a pair of opposite angles A Parallelogram is a rectangle if and only if its diagonals are congruent If a trapezoid is isosceles then each pair of base angles is congruent If a trapezoid has a pair of congruent base angles then it is an isosceles trapezoid A trapezoid is isosceles if and only if it’s diagonals are congruent The Midsegment of a trapezoid is parallel to each base and is half of the sum of the bases lengths. If a quadrilateral is a kite then its diagonals are perpendicular If a quadrilateral is a kite then exactly one pair of opposite angles are congruent The area of a square is a side squared If two polygons are congruent then they have the same area Area of a rectangle= base times height Area of a parallelogram is base times height The area of a triangle is ½ base times height The area of a trapezoid is ½ h(b1+b2) The area of a kite is ½ the product of the diagonals The area of a Rhombus is ½ the product of the diagonals Ratio a to b is written as a/b or a:b In a ration the quotient cannot be zero a/b=c/d then ad=bc b/a=d/c a and d are extremes b and c are means If two polygons are similar then the ratio between their perimeters is equal to their corresponding sides If two polygons are similar then their angles are the same Angle angle postulate If two angles of one triangle are congruent to two angles of another triangle then the two triangles are similar. SIDE SIDE SIDE Postulate If the lengths of two triangles are proportional then the triangles are similar. Side angle Side Postulate If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional then the triangles are similar. If a line parallel to one side of a triangle intersects the other two sides then it divides the two sides proportionally If three lines intersect two transversals then they divide the transversals proportionally If a ray bisects an angle of a triangle then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides. If the altitude is drawn to the hypotenuse of a right triangle then the two triangles formed are similar to the original triangle and to each other In a right triangle the altitude from the right angle divides the hypotenuse into two segments. What is the geometric mean The geometric mean of these two segments is the length of the altitude. In a right Triangle the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. If the square of the hypotenuse is less than the sum of the squares of the other two sides then the triangle is acute If the square of the hypotenuse is greater than the sum of the squares of the other two sides then the triangle is obtuse In a 45 45 90 tiangle the hypotenuse is √2 times as long as each leg In a 60 30 90 the hypotenuse and longer leg is 2 times as long as the shorter leg and the longer leg is √3 times as long as the shorter leg If sinA =x then sin-1x =m angle A If tanA =x then tan-1x =m angle A If cosA =x then cos-1x =m angle A casdf asdfasdf Center: The exact middle of a circle Radius The distance from the circle to the center. If 2 circles have the same radius then they are congruent Diameter The distance across the circle through the center. It equals 2 times the radius. Chord A segment whose endpoints are points on the circle. Secant A line that intersects a circle in two points Tangent a line that intersects with the circle at just one point Minor arcs <180 Major arcs >180 Semicircles =180 If an angle is inscribed in a circle then its measure is half the measure of its intercepted arc. If two inscribed angles of a circle intercept the same arc then the angles are congruent If a right triangle is inscribed in a circle then the hypotenuse is is a diameter of the circle A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary. If a tangent and a chord intersect at a point on a circle then the measure of each angle formed is one half the measure of its intercepted arc If two chords intersect in the interior of a circle then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord If two secant segments share the same endpoint outside a circle then the product of the length of one secant segment and the length of its external segment equals the product of the length of the other secant segment and the length of its external segment. If a secant segment and a tangent segment share an endpoint outside a circle then the product of the lengths of the secant segment and the lengths of its external segment equals the square of the length of the tangent segment. The circumference of a circle is is c=pi D or 2 pi r In a circle the ration of the length of a given arc to the circumference is equal to the ration of the measure of the arc to 360 The Area of a circle is pi time the square of the radius The ratio of the area of a sector of a circle to the area of the circle is equal to the measure of the intercepted arc to 360.