If non-parallel sides of a trapezium are equal, prove that It is Cyclic.
Diagram is also needed.
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____________________________
SOME EXTRA KNOWLEDGE ABOUT QUADRILATERALS:
There are six basic types of quadrilaterals:
Rectangle.
Square.
Parallelogram.
Rhombus.
Trapezium.
Kite.
_______________________________
Important properties of Quadrilaterals:
_____________________________
Properties of a parallelogram
Opposite sides are parallel and congruent.
Opposite angles are congruent.
Adjacent angles are supplementary.
Diagonals bisect each 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 other angles are right and it becomes a rectangle.
______________________________
Properties of a Rectangle
Opposite sides are parallel and congruent.
All angles are right.
The diagonals are congruent and bisect each other (divide each other equally).
Opposite angles formed at the point where diagonals meet are congruent.
A rectangle is a special type of parallelogram whose angles are right.
_____________________________
Properties of a square
All sides and angles are congruent.
Opposite sides are parallel to each other.
The diagonals are congruent.
The diagonals are perpendicular to and bisect each other.
A square is a special type of parallelogram whose all angles and sides are equal.
Also, a parallelogram becomes a square when the diagonals are equal and right bisectors of each other.
_______________________________
Properties of a Rhombus
All sides are congruent.
Opposite angles are congruent.
The diagonals are perpendicular to and bisect each other.
Adjacent angles are supplementary (For eg., ∠A + ∠B = 180°).
A rhombus is a parallelogram whose diagonals are perpendicular to each other.
_____________________________
Properties of a Trapezium
The bases of the trapezium are parallel to each other (MN ⫽ OP).
No sides, angles and diagonals are congruent.
Important formulaes of Quadrilaterals:
_______________________________
Important formulas of parallelograms
Area = L * H
Perimeter = 2(L+B)
______________________________
Important formulas for rectangles
If the length is L and breadth is B, then
Length of the diagonal of a rectangle = √(L2 + B2)
Area = L * B
Perimeter = 2(L+B)
______________________________
Important formulas for Squares
If ‘L’ is the length of the side of a square then length of the diagonal = L √2.
Area = L2.
Perimeter = 4L
_____________________________
Important formulas for a Rhombus
If a and b are the lengths of the diagonals of a rhombus,
Area = (a* b) / 2
Perimeter = 4L
______________________________
Important Formulas for a Trapezium
Area = (1/2) h (L+L2)
Perimeter = L + L1 + L2 + L3
______________________________
HOPE THIS HELPS YOU DII!!! ^_^
____________________________
SOME EXTRA KNOWLEDGE ABOUT QUADRILATERALS:
There are six basic types of quadrilaterals:
Rectangle.
Square.
Parallelogram.
Rhombus.
Trapezium.
Kite.
_______________________________
Important properties of Quadrilaterals:
_____________________________
Properties of a parallelogram
Opposite sides are parallel and congruent.
Opposite angles are congruent.
Adjacent angles are supplementary.
Diagonals bisect each 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 other angles are right and it becomes a rectangle.
______________________________
Properties of a Rectangle
Opposite sides are parallel and congruent.
All angles are right.
The diagonals are congruent and bisect each other (divide each other equally).
Opposite angles formed at the point where diagonals meet are congruent.
A rectangle is a special type of parallelogram whose angles are right.
_____________________________
Properties of a square
All sides and angles are congruent.
Opposite sides are parallel to each other.
The diagonals are congruent.
The diagonals are perpendicular to and bisect each other.
A square is a special type of parallelogram whose all angles and sides are equal.
Also, a parallelogram becomes a square when the diagonals are equal and right bisectors of each other.
_______________________________
Properties of a Rhombus
All sides are congruent.
Opposite angles are congruent.
The diagonals are perpendicular to and bisect each other.
Adjacent angles are supplementary (For eg., ∠A + ∠B = 180°).
A rhombus is a parallelogram whose diagonals are perpendicular to each other.
_____________________________
Properties of a Trapezium
The bases of the trapezium are parallel to each other (MN ⫽ OP).
No sides, angles and diagonals are congruent.
Important formulaes of Quadrilaterals:
_______________________________
Important formulas of parallelograms
Area = L * H
Perimeter = 2(L+B)
______________________________
Important formulas for rectangles
If the length is L and breadth is B, then
Length of the diagonal of a rectangle = √(L2 + B2)
Area = L * B
Perimeter = 2(L+B)
______________________________
Important formulas for Squares
If ‘L’ is the length of the side of a square then length of the diagonal = L √2.
Area = L2.
Perimeter = 4L
_____________________________
Important formulas for a Rhombus
If a and b are the lengths of the diagonals of a rhombus,
Area = (a* b) / 2
Perimeter = 4L
______________________________
Important Formulas for a Trapezium
Area = (1/2) h (L+L2)
Perimeter = L + L1 + L2 + L3
______________________________
HOPE THIS HELPS YOU DII!!! ^_^
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SillySam:
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