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
      \(S = ah =\) \(ab\sin \alpha =\) \({\large\frac{1}{2}\normalsize} {d_1}{d_2}\sin \varphi \)