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Find out how steep SR is in the PQRS shape. We already know how steep PQ and QR are.
If the slope of PQ is 2/3 and the slope of QR is-1/2 , Find the slope of SR so that PQRS is a Parallelogram.
To find the slope of SR so that PQRS is a parallelogram, we can use the property that opposite sides of a parallelogram are parallel and thus have equal slopes.
Given that the slope of PQ is 2/3 and the slope of QR is −1/2, we can use this information to find the slope of SR.
Since PQ and SR are opposite sides of the parallelogram, they must have the same slope. Therefore, the slope of SR is also 2/3.
Hence, the slope of SR is 2/3 to ensure that PQRS is a parallelogram.
Properties of a Parallelogram
A parallelogram is a type of quadrilateral, a polygon with four sides. It has several properties that distinguish it from other quadrilaterals:
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Opposite sides are parallel: In a parallelogram, opposite sides are equal in length and parallel to each other. This means that if you extend one side of the parallelogram, it will never intersect with the other side.
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Opposite angles are congruent: The angles formed between the intersecting sides of a parallelogram are equal in measure. This property implies that the sum of adjacent angles is always 180 degrees.
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Consecutive angles are supplementary: The sum of the measures of consecutive (adjacent) angles in a parallelogram is always 180 degrees.
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Diagonals bisect each other: The diagonals of a parallelogram bisect each other, meaning they intersect at their midpoints. This implies that the line segment formed by joining the midpoints of the diagonals is parallel to and half the length of each diagonal.
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Opposite sides are equal in length: In addition to being parallel, opposite sides of a parallelogram are equal in length.
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Consecutive angles are supplementary: The sum of two consecutive angles of a parallelogram is always 180 degrees.
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Diagonals divide the parallelogram into two congruent triangles: The diagonals of a parallelogram divide it into two congruent triangles.
These properties make the parallelogram a particularly useful shape in geometry and trigonometry, with numerous applications in various fields of mathematics and physics.
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