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Introduction |
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We are familiar with plane figures bounded by straight line segments as sides. They are known as Polygons. Polygon is a word of Greek origin. It means figure with many angles implying many sides. |
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Parallelograms |
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Parallelogram is a quadrilateral whose opposite sides are parallel and equal. A rectangle, a rhombus and a square are considered as parallelograms. |
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Theorem1 |
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The diagonals of a parallelogram bisect each other. |
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Sufficient Conditions for a Quadrilateral to be a Parallelogram |
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If both pairs of opposite sides of a quadrilateral are equal, then the quadrilateral is a parallelogram. |
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Theorem2 |
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If the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram. |
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Theorem3 |
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A quadrilateral is a parallelogram if one pair of opposite sides are equal and parallel. |
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Special Parallelograms |
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Rectangles, rhombuses and squares belong to the set of parallelograms. |
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Theorem4 |
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Recall that the diagonals of a parallelogram bisect each other. Since a rectangle is also a parallelogram, the diagonals of a rectangle also bisect each other. |
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Converse of Theorem4 |
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If two diagonals of a parallelogram are equal, it is a rectangle. |
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Theorem5 |
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The diagonals of a rhombus are perpendicular to each other. |
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Converse of Theorem5 |
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If the diagonals of a parallelogram are perpendicular then it is a rhombus. |
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Theorem6 |
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The diagonals of a square are equal and perpendicular to each other. |
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Converse of Theorem6 |
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If in a parallelogram, the diagonals are equal and perpendicular, then it is a square. |
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Theorem7 |
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The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and equal to half of it. |
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Converse of Theorem7 |
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A straight line drawn through the mid-point of one side and parallel to another side of a triangle bisects the third side. |
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Theorem8 |
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If there are three or more parallel lines and the intercepts made by them on one transversal are equal, the corresponding intercepts of any transversal are also equal. |
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Summary |
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Quadrilateral : A plane closed figure formed by four line segments is called a quadrilateral. |
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Question and Answers |
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