do all sides of a parallelogram have to be equal?
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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.
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Theorem 47: If both pairs of opposite angles of a quadrilateral are equal, then it is a parallelogram. ... Theorem 49: If one pair of opposite sides of a quadrilateral is both equal and parallel, then it is a parallelogram. Theorem 50: If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
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['All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite angles are congruent, and consecutive angles are supplementary).', 'All sides are congruent by definition.', 'The diagonals bisect the angles.']
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No, as a general rule the diagonals of a parallelogram do not bisect each other at right angles. The definition of a parallelogram is a four-sided polygon with opposite sides parallel and equal in length. ... For all parallelograms that are not squares, the diagonals do not intersect at right angles.
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A parallelogram has opposite sides parallel and equal in length. Also opposite angles are equal (angles "A" are the same, and angles "B" are the same). NOTE: Squares, Rectangles and Rhombuses are all Parallelograms!
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All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite sides are congruent, and diagonals bisect each other). All angles are right angles by definition. The diagonals are congruent.
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A parallelogon must have an even number of sides and opposite sides must be equal in length and parallel (hence the name). A less obvious corollary is that all parallelogons have either four or six sides; a four-sided parallelogon is called a parallelogram.
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The diagonals of a parallelogram bisect each other (and conversely: if the diagonals of a quadrilateral bisect each other, it is a parallelogram). If one pair of opposite sides of a quadrilateral is equal and parallel, then the quadrilateral is a parallelogram.
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THEOREM: If a quadrilateral has diagonals which bisect each other, then it is a parallelogram. THEOREM: If a quadrilateral has one set of opposite sides which are both congruent and parallel, then it is a parallelogram. This last method can save time and energy when working a proof!
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If the measures of two angles of a quadrilateral are equal, then the quadrilateral is sometimes a parallelogram. 3. If one pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral is always a parallelogram.
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If the consecutive sides of a parallelogram are equal then it is necessarily a rhombus.
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The diagonals of a parallelogram are not of equal length. They bisect with each other at the point of intersection with equal sides across the point of intersection. This can be proved using the ASA criterion as well. When we divide the parallelogram through two diagonals, we see that four triangles are formed.
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Problem 1: The opposite sides of a parallelogram are both parallel and congruent. The opposite angles of a parallelogram are congruent. ... The consecutive angles of a parallelogram are never complementary. A square is always a rhombus.
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If the diagonals AC and BD of a quadrilateral ABCD intersect O and separate the quadrilateral in four triangle are equal, can you prove ABCD is a parallelogram? Given that all triangles formed by diagonals of the quadrilateral are equal. ... We proved that diagonals of ABCD bisect each other. => ABCD is a parallelogram.
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All the properties of a parallelogram apply (the ones that matter here are parallel sides, opposite angles are congruent, and consecutive angles are supplementary). All sides are congruent by definition. The diagonals bisect the angles.
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The opposite sides of a parallelogram are equal (and conversely: if the opposite sides of a quadrilateral are equal, it is a parallelogram). ... If one pair of opposite sides of a quadrilateral is equal and parallel, then the quadrilateral is a parallelogram.
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All four sides of a rhombus are congruent. Its properties include that each pair of opposite sides is parallel, also making it a parallelogram. ... All rectangles are parallelograms, but not all parallelograms are rectangles. And all of these shapes are quadrilaterals.