How to find a diagonal parallelogram?

Oksana Logunova
Oksana Logunova
April 9, 2013
How to find a diagonal parallelogram?

A parallelogram is a geometric shape, a characteristic feature of which is that its opposite sides are parallel and equal in pairs, and the diagonals in it intersect, and the restraint point divides them in half. Square, rhombus and rectangle are parallelograms.

Diagonal parallelogram

Consider how to find the diagonal of a parallelogram. In the parallelogram:

  • The sum of the angles that are adjacent to one side will always be 180 degrees;
  • The point at which the diagonals intersect is the center of symmetry of the parallelogram.
  • In any quadrilateral, including a parallelogram, the sum of all angles is 360 degrees;
  • The doubled sum of squares of two adjacent sides of a parallelogram is always equal to the sum of the squares of the diagonals.

In order to know how to find a large diagonal parallelogram, you must decide on the letter designation. For example, we have a parallelogram with sides AB and BC.The small letter “a” denotes one length of the parallelogram, and the small letter “c” will be its second length. Small letters d1 d2 denote the diagonal. In order to find the diagonal of the parallelogram:

  • The value of the parallelogram properties helps to find the right solution. Diagonals that are halved at the point of restraint are called bisectrixes. The smaller bisector is for obtuse angles, big for sharp angles. Thus, when considering pairs of triangles derived from one diagonal and two adjacent sides of a geometric figure, the other half of the diagonal is also a median.
  • Triangles that result from the formation of halves of the diagonal and parallel sides of any parallelogram are considered similar, the diagonal also divides such a geometric figure into two triangles, they are symmetrical with respect to the base and absolutely identical.
  • To find the large diagonal of the parallelogram, it is necessary to use the generally accepted formula, which tells about the ratio of the sum of squares of lengths of the sides, which doubles and the sum of squares of two diagonals. The formula will look like this: d1² + d2² = 2x (a² + b²).
  • If the large diagonal is d2, then the formula will look like this: d2 = {2x (a² + b²) - d1²}.

Consider an example of how to find the length of the diagonal of a parallelogram. Suppose that a parallelogram has the length of the sides: a = 3, c = 8. It is necessary to find the diagonal that is larger, while it will be known that it is less than three cm. Diagonal. First, we write the formula in general, it will look like: d1² + d2² = 2 x (9 + 64) = 146, then we express the length of the smaller diagonal: d1 = d2 - 3, substituting this expression in the first formula, we get: (d2 - 3) ² + d2² = 146

  • We square the value in brackets, we get: d2² - 6x d2 + 9 + d2² = 14, 2x d2² - 6x d2 -135 = 0
  • The resulting quadratic equation is solved using a discriminant. Thus, the diagonal is 9.85 and it is a positive value.

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