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properties of parallelograms properties of parallelograms in euclidean geometry a parallelogram is a simple non self-intersecting quadrilateral with two pairs of parallel sides the opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure the congruence of opposite sides and opposite angles is a direct consequence of the euclidean parallel postulate and neither condition can be proven without appealing to the euclidean parallel postulate or one of its equivalent formulations the threedimensional counterpart of a parallelogram is a parallelepiped.the etymology in greek a shape of parallel lines reflects the definition properties opposite sides of a parallelogram are parallel by definition and so will never intersect the area of a parallelogram is twice the area of a triangle created by one of its diagonals the area of a parallelogram is also equal to the magnitude of the vector cross product of two adjacent sides any line through the midpoint of a parallelogram bisects the area 3 any non-degenerate affine transformation takes a parallelogram to another parallelogram a parallelogram has rotational symmetry of order 2 through 180° if it also has two lines of reflectional symmetry then it must be a rhombus or an oblong know more about linear pair of angles math.edurite.com page 1/3

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the perimeter of a parallelogram is 2a b where a and b are the lengths of adjacent sides the sum of the distances from any interior point of a parallelogram to the sides is independent of the location of the point this is an extension of viviani s theorem the converse also holds if the sum of the distances from a point in the interior of a quadrilateral to the sides is independent of the location of the point then the quadrilateral is a parallelogram types of parallelogram rhomboid ­ a quadrilateral whose opposite sides are parallel and adjacent sides are unequal and whose angles are not right angles,traditionally in two-dimensional geometry a rhomboid is a parallelogram in which adjacent sides are of unequal lengths and angles are oblique.a parallelogram with sides of equal length equilateral is a rhombus but not a rhomboid.a parallelogram with right angled corners is a rectangle but not a rhomboid rectangle ­ a parallelogram with four angles of equal size a rectangle is any quadrilateral with four right angles another name is equiangular quadrilateral since equiangular means that all of its angles are equal 360°/4 90° it can also be defined as a parallelogram containing a right angle the term oblong is occasionally used to refer to a non-square rectangle 1 2 a rectangle with vertices abcd would be denoted as abcd rhombus ­ a parallelogram with four sides of equal length a rhombus plural rhombi or rhombuses is a simple non self-intersecting quadrilateral whose four sides all have the same length another name is equilateral quadrilateral since equilateral means that all of its sides are equal the rhombus is often called a diamond after the diamonds suit in playing cards or a lozenge though the latter sometimes refers specifically to a rhombus with a 45° angle square ­ a parallelogram with four sides of equal length and four angles of equal size right angles a square is a regular quadrilateral this means that it has four equal sides and four equal angles 90degree angles or right angles 1 it can also be defined as a rectangle in which two adjacent sides have equal length a square with vertices abcd would be denoted abcd read more about parallelogram properties math.edurite.com page 2/3

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thank you math.edurite.com

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