In this indict on simple geometry concepts, us cover the types and properties of quadrilaterals: Parallelogram, rectangle, square, rhombus, trapezium.
You are watching: The diagonals of a square are perpendicular
Definition:
A quadrilateral is a straightforward closed figure with 4 sides.
Types that quadrilaterals
There space five species of quadrilaterals.
ParallelogramRectangleSquareRhombusTrapezium
One common property of all quadrilaterals is the the amount of all their angles equates to 360°.
Let united state look right into the nature of different quadrilaterals.
Parallelogram
Properties of a parallelogramOpposite sides are parallel and congruent.Opposite angles are congruent.Adjacent angles room supplementary.Diagonals bisect each other and also each diagonal line divides the parallelogram into two congruent triangles.If among the angles of a parallelogram is a best angle then all other angles are right and also it i do not care a rectangle.
Important formulas of parallelogramsArea = together * HPerimeter = 2(L+B)
Rectangles
Properties of a RectangleOpposite sides space parallel and also congruent.All angles space right.The diagonals space congruent and also bisect each various other (divide each other equally).Opposite angles developed at the suggest where diagonals meet are congruent.A rectangle is a special type of parallelogram whose angles space right.
Important formulas for rectanglesIf the size is L and breadth is B, then
Length of the diagonal of a rectangle = √(L2 + B2)
Area = together * BPerimeter = 2(L+B)
Squares
Properties of a squareall sides and angles room congruent.Opposite sides are parallel to every other.The diagonals are congruent.The diagonals space perpendicular to and also bisect each other.A square is a special kind of parallelogram whose every angles and also sides are equal.Also, a parallelogram becomes a square when the diagonals are equal and also right bisectors of each other.
Important formulas for SquaresIf ‘L’ is the length of the next of a square then length of the diagonal line = l √2.Area = L2.Perimeter = 4L
Rhombus
Properties that a RhombusAll sides room congruent.Opposite angles space congruent.The diagonals are perpendicular to and bisect each other.Adjacent angles space supplementary (For eg., ∠A + ∠B = 180°).A rhombus is a parallelogram whose diagonals space perpendicular to every other.
Important formulas because that a Rhombus
If a and also b are the lengths that the diagonals of a rhombus,
Area = (a* b) / 2Perimeter = 4L
Trapezium
Properties that a TrapeziumThe bases that the trapezium are parallel come each other (MN ⫽ OP).No sides, angles and also diagonals room congruent.
See more:
What Was Made Illegal In England In 1439 : Kissing Banned In England!Important Formulas for a TrapeziumArea = (1/2) h (L+L2)Perimeter = together + L1 + L2 + L3
Summary of properties
Summarizing what we have learnt so much for straightforward reference and also remembrance:
| S.No. | Property | Parallelogram | Rectangle | Rhombus | Square |
| 1 | All sides are congruent | ✕ | ✕ | ✓ | ✓ |
| 2 | Opposite sides space parallel and congruent | ✓ | ✓ | ✓ | ✓ |
| 3 | All angles room congruent | ✕ | ✓ | ✕ | ✓ |
| 4 | Opposite angles room congruent | ✓ | ✓ | ✓ | ✓ |
| 5 | Diagonals space congruent | ✕ | ✓ | ✕ | ✓ |
| 6 | Diagonals room perpendicular | ✕ | ✕ | ✓ | ✓ |
| 7 | Diagonals bisect each other | ✓ | ✓ | ✓ | ✓ |
| 8 | Adjacent angles room supplementary | ✓ | ✓ | ✓ | ✓ |
Continue learning more about:– nature of Lines and also Angles– Properties and also formulas of Circles– types of Triangles and Properties
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