Quadrilaterals: SSC CGL Quantitative Aptitude

Formulas (4)

• Angle sum and the diagonals of any quadrilateral · Quadrilateral angles
  $$\angle A + \angle B + \angle C + \angle D = 360^\circ \qquad \text{cyclic: } \angle A + \angle C = \angle B + \angle D = 180^\circ$$
• Trapezium: area and the triangles made by its diagonals · Trapezium
  $$\text{area} = \frac{1}{2}(a + b)h \qquad AE : EC = AB : CD \qquad \frac{\text{area } ABE}{\text{area } CDE} = \frac{AB^2}{CD^2}$$
• Parallelogram: opposite sides, angles and diagonals · Parallelogram ABCD
  $$AB = CD,\ BC = DA \qquad \angle A = \angle C,\ \angle A + \angle B = 180^\circ \qquad AO = OC,\ BO = OD$$
• Rhombus and kite: equal sides give congruent halves · Rhombus side from its diagonals
  $$\text{side}^2 = \left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2$$

Watch out for (10)

• Sharing 360° when one angle is already known
  → Angle sum and the diagonals of any quadrilateral
• Using the cyclic rule on any quadrilateral
  → Angle sum and the diagonals of any quadrilateral
• Giving the side ratio for an area ratio
  → Trapezium: area and the triangles made by its diagonals
• Using a slanted side as the height
  → Trapezium: area and the triangles made by its diagonals
• Calling a trapezium a parallelogram
  → Parallelogram: opposite sides, angles and diagonals
• Giving a parallelogram perpendicular or equal diagonals
  → Parallelogram: opposite sides, angles and diagonals
• Taking a diagonal as an angle bisector
  → Parallelogram: opposite sides, angles and diagonals
• Taking the kite's symmetry line from the wrong diagonal
  → Rhombus and kite: equal sides give congruent halves
• Giving a rhombus equal diagonals
  → Rhombus and kite: equal sides give congruent halves
• Putting whole diagonals into Pythagoras
  → Rhombus and kite: equal sides give congruent halves