Which Of The Following Quadrilaterals Have Diagonals That Are Perpendicular To Each Other

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

You are watching: Which of the following quadrilaterals have diagonals that are perpendicular to each other

Definition:

A quadrilateral is a straightforward closed figure with four sides.

Types the quadrilaterals

There room five species of quadrilaterals.

ParallelogramRectangleSquareRhombusTrapezium

One typical property of all quadrilaterals is the the amount of all your angles equates to 360°.

Let united state look right into the properties of various quadrilaterals.

Parallelogram

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

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

Rectangles

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

Important formulas because that rectanglesIf the length is L and also breadth is B, then

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

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

Squares

Properties that a squareall sides and also angles space congruent.Opposite sides room parallel to each other.The diagonals space congruent.The diagonals space perpendicular to and bisect each other.A square is a special kind of parallel whose all angles and also sides room equal.Also, a parallel becomes a square once the diagonals are equal and also right bisectors of each other.

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

Rhombus

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

Important formulas because that a Rhombus

If a and b space the lengths the the diagonals of a rhombus,

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

Trapezium

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

See more: What Is The Function Of Rugae ? What Is The Function Of The Rugae In A Fetal Pig

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

Summary the properties

Summarizing what we have actually learnt so far for basic reference and also remembrance:

S.No.	Property	Parallelogram	Rectangle	Rhombus	Square
1	All sides are congruent	✕	✕	✓	✓
2	Opposite sides are parallel and congruent	✓	✓	✓	✓
3	All angles room congruent	✕	✓	✕	✓
4	Opposite angles are congruent	✓	✓	✓	✓
5	Diagonals room congruent	✕	✓	✕	✓
6	Diagonals are perpendicular	✕	✕	✓	✓
7	Diagonals bisect every other	✓	✓	✓	✓
8	Adjacent angles are supplementary	✓	✓	✓	✓

Continue learning more about:– nature of Lines and Angles– Properties and also formulas that Circles– species of Triangles and also Properties

13/11/2021

Which of the following quadrilaterals have diagonals that are perpendicular to each other