Quadrilaterals B Ludhiana
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Govt. Sen. Sec. School Samrala
Presentation On Quadrilaterals Made By Jatinder Saddi (Math’s Teacher)
QUADRILATERAL Quadrilateral:The plane enclosed by four sides (lines, line segments) is called quadrilateral.
In figure (1) and (2) the sides AB,BC,CD,DA have enclosed a plane, hence these are quadrilaterals. In figure (1) AB,BC,CD,DA are straight lines while in figure (2) these are line segments.
Facts About Quadrilateral
A quadrilateral has four sides and four angles i.e. quadrilateral ABCD have four sides AB, BC,CD,DA and four angles ∠A,∠B,∠C,∠D. The sum total of four angles of a quadrilateral is 360º , i.e. ∠A+ ∠B+ ∠C+ ∠D=360º.
The line segment obtained by joining opposite points is called the diagonal of the quadrilateral. A quadrilateral has two diagonals, these are AC and BD.
SPECIAL TYPES OF QUARILATERAL TRAPEZIUM PARALLELOGRAM RHOMBUS RECTANGLE and SQUARE
TRAPEZIUM Trapezium:A quadrilateral in which a pair of opposite sides are parallel is called trapezium.
Quadrilateral ABCD is a trapezium because AB||DC.
PROPERTY OF TRAPEZIUM In trapezium ABCD, AB||DC and AD intersects them. Therefore ∠A+ ∠D =180º (∠A and ∠D are interior angles formed on one side of the intersecting line) Similarly ∠B+ ∠D =180º
PARALLELOGRAM PARALLELOGRAM:If both the pair of opposite sides of a quadrilateral are parallel, then it is called a parallelogram.
Quadrilateral ABCD is a parallelogram because AB||DC and AD||BC.
PROPERTIES OF THE PARALLELOGRAM
Properties:In a parallelogram opposite sides are equal, i.e. in parallelogram ABCD, AB=CD and AD=BC. In a parallelogram, opposite angles are equal, i.e. in parallelogram ABCD, ∠A=∠C and ∠B=∠D. The diagonals of a parallelogram are bisectors of each other, i.e. in parallelogram AO=OC and BO=OD.
RHOMBUS RHOMBUS:A rhombus is a parallelogram with a pair of its adjacent sides equal. Quadrilateral ABCD is rhombus because AB|| DC ,AD||BC and AB=BC=CD=DA.
PROPERTIES OF A RHOMBUS •
• •
All the sides of a rhombus are equal i.e. AB=BC=CD=DA. Opposite angles are equal, i.e. ∠A=∠C, ∠B=∠D. The diagonals are rightbisector of each other i.e. AC and BD intersect in such a way that AO=OC, BO=OD and AC⊥BD.
RECTANGLE RECTANGLE:A rectangle is a parallelogram with one of its angles a right angle. Parallelogram ABCD is a rectangle because ∠A= 90º
PROPERTIES OF RECTANGLE •
•
• •
The opposite sides of a rectangle are equal, i.e. AB=CD and AD=BC. Each angle of the rectangle is 90º, i.e. ∠A= ∠B= ∠C= ∠D= 90º. (using property of parallel lines) The diagonals of the rectangle are equal, i.e. AC=BD. The diagonals of the rectangle bisect each other, i.e. AO=OC and BO=OD.
SQUARE SQUARE:A rectangle with equal adjacent sides is called a square.
Rectangle ABCD is a Square because AB=AD.
PROPERTIES OF SQUARE •
•
• •
All the sides of the square are equal, i.e. AB=BC=CD=DA. Each angle of the square is right angle, i.e. ∠A= ∠B= ∠C= ∠D= 90º. Diagonals of the square are equal, i.e. AC=BD. Diagonals of the square are right bisectors of each other, i.e. AC⊥BD and OA=OB=OC=OD.
THANK YOU VERY MUCH
Presentation On Quadrilaterals Made By Jatinder Saddi (Math’s Teacher)
QUADRILATERAL Quadrilateral:The plane enclosed by four sides (lines, line segments) is called quadrilateral.
In figure (1) and (2) the sides AB,BC,CD,DA have enclosed a plane, hence these are quadrilaterals. In figure (1) AB,BC,CD,DA are straight lines while in figure (2) these are line segments.
Facts About Quadrilateral
A quadrilateral has four sides and four angles i.e. quadrilateral ABCD have four sides AB, BC,CD,DA and four angles ∠A,∠B,∠C,∠D. The sum total of four angles of a quadrilateral is 360º , i.e. ∠A+ ∠B+ ∠C+ ∠D=360º.
The line segment obtained by joining opposite points is called the diagonal of the quadrilateral. A quadrilateral has two diagonals, these are AC and BD.
SPECIAL TYPES OF QUARILATERAL TRAPEZIUM PARALLELOGRAM RHOMBUS RECTANGLE and SQUARE
TRAPEZIUM Trapezium:A quadrilateral in which a pair of opposite sides are parallel is called trapezium.
Quadrilateral ABCD is a trapezium because AB||DC.
PROPERTY OF TRAPEZIUM In trapezium ABCD, AB||DC and AD intersects them. Therefore ∠A+ ∠D =180º (∠A and ∠D are interior angles formed on one side of the intersecting line) Similarly ∠B+ ∠D =180º
PARALLELOGRAM PARALLELOGRAM:If both the pair of opposite sides of a quadrilateral are parallel, then it is called a parallelogram.
Quadrilateral ABCD is a parallelogram because AB||DC and AD||BC.
PROPERTIES OF THE PARALLELOGRAM
Properties:In a parallelogram opposite sides are equal, i.e. in parallelogram ABCD, AB=CD and AD=BC. In a parallelogram, opposite angles are equal, i.e. in parallelogram ABCD, ∠A=∠C and ∠B=∠D. The diagonals of a parallelogram are bisectors of each other, i.e. in parallelogram AO=OC and BO=OD.
RHOMBUS RHOMBUS:A rhombus is a parallelogram with a pair of its adjacent sides equal. Quadrilateral ABCD is rhombus because AB|| DC ,AD||BC and AB=BC=CD=DA.
PROPERTIES OF A RHOMBUS •
• •
All the sides of a rhombus are equal i.e. AB=BC=CD=DA. Opposite angles are equal, i.e. ∠A=∠C, ∠B=∠D. The diagonals are rightbisector of each other i.e. AC and BD intersect in such a way that AO=OC, BO=OD and AC⊥BD.
RECTANGLE RECTANGLE:A rectangle is a parallelogram with one of its angles a right angle. Parallelogram ABCD is a rectangle because ∠A= 90º
PROPERTIES OF RECTANGLE •
•
• •
The opposite sides of a rectangle are equal, i.e. AB=CD and AD=BC. Each angle of the rectangle is 90º, i.e. ∠A= ∠B= ∠C= ∠D= 90º. (using property of parallel lines) The diagonals of the rectangle are equal, i.e. AC=BD. The diagonals of the rectangle bisect each other, i.e. AO=OC and BO=OD.
SQUARE SQUARE:A rectangle with equal adjacent sides is called a square.
Rectangle ABCD is a Square because AB=AD.
PROPERTIES OF SQUARE •
•
• •
All the sides of the square are equal, i.e. AB=BC=CD=DA. Each angle of the square is right angle, i.e. ∠A= ∠B= ∠C= ∠D= 90º. Diagonals of the square are equal, i.e. AC=BD. Diagonals of the square are right bisectors of each other, i.e. AC⊥BD and OA=OB=OC=OD.
THANK YOU VERY MUCH
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