proof to show that opposite sides of a parallelogram are congruent?
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THEOREM: If a quadrilateral has 2 sets of opposite sides congruent, then it is a parallelogram. ... 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.
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DEFINITION: A parallelogram is a quadrilateral with both pairs of opposite sides parallel. THEOREM: If a quadrilateral has 2 sets of opposite sides congruent, then it is a parallelogram. THEOREM: If a quadrilateral has 2 sets of opposite angles congruent, then it is a parallelogram.
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Theorem 16.5: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.
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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. In summary, all squares are rectangles, but not all rectangles are squares. All rectangles are parallelograms, but not all parallelograms are rectangles.
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Of the statements given, the one that is not always true about a parallelogram is that the diagonals are congruent. By the definition of a...
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The opposite sides of a parallelogram are equal. ABCD is a parallelogram. To prove that AB = CD and AD = BC. ... Hence AB = CD and BC = AD (matching sides of congruent triangles).
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Parallelograms: The Two Pairs of Opposite Angles are Congruent. 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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The diagonals of a parallelogram are sometimes congruent. The diagonals of a rhombus are always perpendicular. The consecutive angles of a parallelogram are never complementary.
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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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Properties of a Parallelogram The parallelogram's opposite angles are congruent to each other and its consecutive angles are supplementary to each other. The parallelogram's diagonals AC and BD bisect each other and its diagonals form two congruent triangles.
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A quadrilateral is a four-sided flat shape. A parallelogram is a quadrilateral with two pairs of opposite and parallel sides. To prove a quadrilateral is a parallelogram, you must use one of these five ways. ... Prove that one pair of opposite sides is both congruent and parallel.
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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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Parallelogram Theorem #1: Each diagonal of a parallelogram divides the parallelogram into two congruent triangles. Parallelogram Theorem #2: The opposite sides of a parallelogram are congruent. ... You can show that alternate interior angles are congruent and hence lines are parallel for this part of the proof.
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Opposite sides are parallel to each other. The diagonals are congruent. The diagonals are perpendicular to and bisect each other. ... Also, a parallelogram becomes a square when the diagonals are equal and right bisectors of each other.
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['Opposite sides are congruent (AB = DC).', 'Opposite angels are congruent (D = B).', 'Consecutive angles are supplementary (A + D = 180°).', 'If one angle is right, then all angles are right.', 'The diagonals of a parallelogram bisect each other.', 'Each diagonal of a parallelogram separates it into two congruent triangles.']
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THEOREM: If a quadrilateral is a parallelogram, it has 2 sets of opposite angles congruent. THEOREM: If a quadrilateral is a parallelogram, it has consecutive angles which are supplementary.
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Properties of a Rhombus Opposite angles are congruent. The diagonals are perpendicular to and bisect each other.