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If a quadrilateral is a trapezoid, then the mid segment is parallel to the bases, and the length of the mid segment is half the sum of the lengths of the bases

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If a quadrilateral is an isosceles trapezoid, then its diagonals are congruent

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If a quadrilateral is an isosceles trapezoid, then each pair of base angles is congruent

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base angles: the 2 angles that share a base; trapezoids have 2 pairs of base angles

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base angles: the 2 angles that share a base; trapezoids have 2 pairs of base angles

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legs: the nonparallel sides of a trapezoid

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legs: the nonparallel sides of a trapezoid

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trapezoid: a quadrilateral with exactly one pair of parallel sides called bases

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trapezoid: a quadrilateral with exactly one pair of parallel sides called bases

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If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle

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If one diagonal of a parallelogram bisects a pair of opposite angles, then the parallelogram is a rhombus

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If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus

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If a parallelogram is a rectangle, then its diagonals are congruent

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If a parallelogram is a rhombus, then each diagonal bisects a pair of opposite angles

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If a parallelogram is a rhombus, then its diagonals are perpendicular

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If one pair of opposite sides of a quadrilateral is both congruent and parallel, then the quadrilateral is a parallelogram

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If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram

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If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram

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If an angle of a quadrilateral is supplementary to both of its consecutive angles, then the quadrilateral is a parallelogram

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If both paris of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram

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If 3 or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal

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If a quadrilateral is a parallelogram, then its diagonals bisect each other

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If a quadrilateral is a parallelogram, then its opposite angles are congruent

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If a quadrilateral is a parallelogram, then its consecutive angles are supplementary

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consecutive angles: angles of a polygon that share a side

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consecutive angles: angles of a polygon that share a side

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opposite angles: angles that do not share a side

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opposite angles: angles that do not share a side

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opposite sides: sides that do not share a verte

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opposite sides: sides that do not share a verte

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parallelogram: a quadrilateral with both pairs of opposite sides parallel

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parallelogram: a quadrilateral with both pairs of opposite sides parallel

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The sum of the measures the exterior angles of a polygon, on at each vertex, is 360

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Corollary to the Polygon Angle-Sum Theorem

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Corollary to the Polygon Angle-Sum Theorem

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regular polygon: a polygon that is both equilateral and equiangular

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regular polygon: a polygon that is both equilateral and equiangular

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equiangular polygon: is a polygon with all angles congruent

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equiangular polygon: is a polygon with all angles congruent

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equilateral polygon: a polygon with all sides congruent

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equilateral polygon: a polygon with all sides congruent

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The sum of the measures of the interior angles of an n-gon is (n-2) 180