are opposite sides of a parallelogram always congruent?
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The opposite angles of a parallelogram are congruent. The consecutive angles are supplementary. ... The diagonals of a parallelogram are sometimes congruent. The diagonals of a rhombus are always perpendicular.
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A parallelogram is defined as a quadrilateral where the two opposite sides are parallel. One of the properties of parallelograms is that the opposite angles are congruent, as we will now show.
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Opposite sides are congruent. Opposite angles are congruent. Consecutive angles are supplementary. The diagonals bisect each other.
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Yes, if both pairs of opposite angles are congruent, then you have a parallelogram. These are all sufficient conditions to have a parallelogram.
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A parallelogram is a quadrilateral with both pairs of opposite sides parallel. ... THEOREM: If a quadrilateral is a parallelogram, it has 2 sets of opposite sides congruent. * THEOREM: If a quadrilateral is a parallelogram, it has 2 sets of opposite angles congruent.
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If a quadrilateral is a parallelogram, then its opposite sides are congruent. If a quadrilateral is a parallelogram, then its opposite angles are congruent. If a quadrilateral is a parallelogram, then its diagonals bisect each other.
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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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Prove that, opposite sides of a parallelogram are equal. By ASA criterion of concurrency triangle ADC is congruent to triangle ABC.
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All sides and angles are congruent. Opposite sides are parallel to each other. The diagonals are congruent. The diagonals are perpendicular to and bisect each other.
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To prove that the opposite angles of a parallelogram are equal. Construction: Draw a parallelogram ABCD. Join BD. So triangles ABD and BCD are congruent.
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DEFINITION: A parallelogram is a quadrilateral with both pairs of opposite sides parallel. THEOREM: If a quadrilateral is a parallelogram, it has 2 sets of opposite sides congruent. ... THEOREM: If a quadrilateral has 2 sets of opposite angles congruent, then it is a parallelogram.
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If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. If — AB ≅ — CD and — BC ≅ — DA , then 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). ... The diagonals bisect the angles. The diagonals are perpendicular bisectors of each other.
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Prove that opposite sides of a parallelogram are congruent. ... By the same token, segment AB is parallel to segment DC according to the definition of a parallelogram. Line AC is a transversal for segment BC and segment AD. This transversal creates alternate interior angles 1 and 4 which are equal as shown below.
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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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['The opposite angles of a parallelogram are equal.', 'The opposite sides of a parallelogram are equal.', 'The diagonals of a parallelogram bisect each other.']
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If the opposite sides of a (convex) quadrilateral are equal, then the quadrilateral is a parallelogram. Prove this result using congruence in the figure to the right, where the diagonal AC has been joined.