are all sides of a parallelogram congruent?
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One special kind of polygons is called a parallelogram. It is a quadrilateral where both pairs of opposite sides are parallel. If we have a parallelogram where all sides are congruent then we have what is called a rhombus.
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We have proved that the opposite sides of a parallelogram are equal, so if two adjacent sides are equal, then all four sides are equal and it is a rhombus. If two adjacent sides of a parallelogram are equal, then it is a rhombus. ... A quadrilateral whose diagonals bisect each other at right angles is a rhombus.
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Consecutive angles of a parallelogram are congruent. Diagonals of a parallelogram bisect each other. The four angles of a rhombus are right angles.
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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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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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So opposite sides are congruent and quadrilateral MNOP is a parallelogram. Also, adjacent sides are congruent, so parallelogram MNOP is a rhombus. 1.
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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 2 sets of opposite angles congruent, then it is a parallelogram. THEOREM: If a quadrilateral has consecutive angles which are supplementary, then it is a parallelogram.
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Theorem 1: In a parallelogram, the opposite sides are of equal length. Theorem 2: If the opposite sides in a quadrilateral are the same length, then the figure is a parallelogram. Theorem 3: A quadrilateral is a parallelogram if and only if the diagonals bisect each other.
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It is a quadrilateral where both pairs of opposite sides are parallel. If we have a parallelogram where all sides are congruent then we have what is called a rhombus. The properties of parallelograms can be applied on rhombi. ... In an isosceles trapezoid the diagonals are always congruent.
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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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Another quadrilateral that you might see is called a rhombus. 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.
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The correct answer is: Congruent triangles. Explanation: Consider the top and bottom sides of the parallelogram parallel lines.
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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 adjacent sides of a parallelogram are equal, then the parallelogram is a rhombus. In a rhombus, the diagonals bisect each other and are perpendicular to each other.
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Student: We need to say that they are parallel and that in a square all four sides are congruent while in a rectangle only the opposite sides are congruent. ... We could also say that a rectangle is a parallelogram with four right angles, while a square is a parallelogram with four congruent sides and four right angles.
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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.