Elementary Geometry

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Sides of a parallelogram: \(a\), \(b\)
Diagonals of a parallelogram: \({d_1},\) \({d_2}\)
Consecutive angles: \(\alpha\), \(\beta\)
Angle between the diagonals: \(\varphi\)
Perimeter: \(P\)
Area: \(S\)
Altitude: \(h\)
  1. A parallelogram is a quadrilateral with two pairs of parallel sides.
  2. Parallelogram
  3. In a paralellogram, the opposite sides are equal and the opposite angles are equal.
  4. The sum of the consecutive angles of a parallelogram is equal to \(180^\circ:\)
    \(\alpha + \beta = 180^\circ\)
  5. A parallelogram in which all four angles are right angles is called a rectangle. A parallelogram in which all four sides are equal is called a rhombus.
  6. Relationship between the sides and the diagonals of a parallelogram
    \(d_1^2 + d_2^2 =\) \( 2\left( {{a^2} + {b^2}} \right)\)
  7. Altitude of a parallelogram
    \(h = b\sin \alpha =\) \( b\sin \beta\)
  8. Perimeter of a parallelogram
    \(P = 2\left({a + b} \right)\)
  9. Area of a parallelogram
    \(S = ah =\) \(ab\sin \alpha =\) \({\large\frac{1}{2}\normalsize} {d_1}{d_2}\sin \varphi \)