SQUARE

SQUARE

• The diagonals of a square bisect each other and meet at 90°
• The diagonals of a square bisect its angles.
• The diagonals of a square are perpendicular.
• Opposite sides of a square are both parallel and equal in length.
• All four angles of a square are equal.
• All four sides of a square are equal.
• The diagonals of a square are equal.
• The perimeter of the square = 4a (* a is the length of any one side)
• The area of the square = a x a

Bibliography :

• Web Page of BBC
• Wikipedia 
• Web Page of Math Open Reference

RECTANGLE

RECTANGLE

• All angles are equal.
• Alternate sides are equal.
• Its centre is equidistant from its vertices, hence it has a circumcircle
• Its axes of symmetry bisect opposite sides.
• Diagonals are equal in length.
• The perimeter of the rectangle = 2(a+b)   (*a is the base length and b is the side lenght)
• The area of the rectangle = a x b

Bibliography :

• Web Page of BBC
• Wikipedia 

RHOMBUS

RHOMBUS

• All sides are equal.
• Alternate angles are equal.
• Its centre is equidistant from its sides, hence it has an incircle.
• Its axes of symmetry bisect opposite angles.
• Diagonals intersect at equal angles.
• The perimeter of rhombus = 4a   (*a is the side length)
• The area of rhombus = h x s = s² sin(A) =  s² sin(B) = (p × q)/2 (*s is a side lenght of rhombus, h is a height of rhombus, p is a long diagonal of rhombus, q is a short diagonal of rhombus)

Bibliography :

• Web Page of BBC
• Wikipedia 
• Web page of Mathwords

PARALLELOGRAM

PARALLELOGRAM

• Diagonally opposite angles are equal. 
• Opposite sides are of equal length.
• Opposite sides are parallel.
• The diagonals bisect each other.
• It has no lines of symmetry.
• Order of rotational symmetry: 2.
• The perimeter of the parallelogram = 2(a+b)   (*a is the base length and b is the side lenght)
• The area of the parallelogram = b x h     (*b is the lenght of any one side and h is at right angles to b )

Bibliography :

• Web Page of BBC
• Web Side of Mathsisfun 

TRAPEZOID AND ISOSCELES TRAPEZOID

TRAPEZOID

• The bases are parallel by definition.
• Each lower base angle is supplementary to the upper base angle on the same side.
• the perimeter of trapezoid = a+b+c+d (*the sum of all side lengths)
• The area of trapezoid = (a+b/2) × h (*average of the two base lengths times the altitude)

ISOSCELES TRAPEZOID

• The diagonals have the same length.
• The base angles have the same measure.
• An isosceles triangle is formed by the base and the extensions of the legs. 
• The segment that joins the midpoints of the parallel sides is perpendicular to them.
• Opposite angles are supplementary

Bibliography : 

• Web Page of BBC
• Web Side of Mathsisfun 

KITE

KITE

• Two pairs of equal adjacent sides
• One pair of equal opposite angles
• An axis of symmetry through one pair of opposite angles
• Inscribed circle
• The perimeter of kite = 2(a+b) (* a and b are side lengths )
• The area of kite = (p x q)/2  (* p and q are the lengths of the diagonals )

Bibliography : 

• Web Page of BBC
• Web Side of Mathsisfun 

SPECIAL QUADRILATERALS

SPECIAL QUADRILATERALS

    

     A quadrilateral is a polygon with four sides (or edges) and four vertices or corners. The origin of the word "quadrilateral" is the two Latin words quadri, a variant of four, and latus, meaning "side."

      In this chapter, you have studied the seven special types of quadrilaterals shown at the right. Notice that each shape has all the properties of the shapes linked above it.  For instance, squares have the properties of rhombuses, rectangles, parallelograms, and quadrilaterals.