In this indict on an easy geometry concepts, we cover the varieties and nature of quadrilaterals: Parallelogram, rectangle, square, rhombus, trapezium.

You are watching: The diagonals of a parallelogram are perpendicular

Definition:

A quadrilateral is a simple closed figure with four sides.

Types the quadrilaterals

There space five types of quadrilaterals.

ParallelogramRectangleSquareRhombusTrapezium

One common property of every quadrilaterals is the the sum of all their angles amounts to 360°.

Let us look into the properties of various quadrilaterals.

Parallelogram

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Properties of a parallelogramOpposite sides room parallel and congruent.Opposite angles room congruent.Adjacent angles room supplementary.Diagonals bisect each other and each diagonal divides the parallelogram into two congruent triangles.If among the angles of a parallel is a appropriate angle climate all various other angles are right and it i do not care a rectangle.

Important formulas of parallelogramsArea = together * HPerimeter = 2(L+B)

Rectangles

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Properties of a RectangleOpposite sides are parallel and also congruent.All angles are right.The diagonals are congruent and bisect each other (divide each other equally).Opposite angles created at the allude where diagonals satisfy are congruent.A rectangle is a special kind of parallelogram whose angles room right.

Important formulas for rectanglesIf the size is L and also breadth is B, then

Length that the diagonal line of a rectangle = √(L2 + B2)

Area = l * BPerimeter = 2(L+B)

Squares

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Properties the a squareall sides and angles space congruent.Opposite sides room parallel to every other.The diagonals space congruent.The diagonals are perpendicular to and also bisect every other.A square is a special form of parallelogram whose every angles and also sides are equal.Also, a parallelogram becomes a square as soon as the diagonals space equal and right bisectors of each other.

Important formulas because that SquaresIf ‘L’ is the size of the side of a square then size of the diagonal = l √2.Area = L2.Perimeter = 4L

Rhombus

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Properties of a RhombusAll sides space congruent.Opposite angles room congruent.The diagonals space perpendicular to and bisect every other.Adjacent angles are supplementary (For eg., ∠A + ∠B = 180°).A rhombus is a parallelogram whose diagonals room perpendicular to every other.

Important formulas for a Rhombus

If a and also b are the lengths that the diagonals the a rhombus,

Area = (a* b) / 2Perimeter = 4L

Trapezium

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Properties the a TrapeziumThe bases of the trapezium room parallel come each other (MN ⫽ OP).No sides, angles and diagonals space congruent.

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Important Formulas for a TrapeziumArea = (1/2) h (L+L2)Perimeter = together + L1 + L2 + L3

Summary that properties

Summarizing what we have actually learnt so much for easy reference and also remembrance:

S.No.PropertyParallelogramRectangleRhombusSquare
1All sides are congruent
2Opposite sides room parallel and congruent
3All angles space congruent
4Opposite angles room congruent
5Diagonals are congruent
6Diagonals are perpendicular
7Diagonals bisect each other
8Adjacent angles space supplementary

Continue learning much more about:– nature of Lines and Angles– Properties and formulas the Circles– varieties of Triangles and Properties


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