How to Memorize the Properties of Quadrilaterals
Quadrilaterals : How do each differ from one another ?
Any foursided closed figures can be called quadrilaterals. But when the sides, angles and diagonals follow specific properties, they turn out to be quadrilaterals recognized by specific names rather than just quadrilaterals.
Here, we would be discussing about Parallelograms followed by Rectangles, Rhombuses and Squares and also Trapeziums.
The main points we would be focusing are :
 Sides
 Angles
 Diagonals
Parallelogram
A parallelogram is formed by connecting two congruent triangles ( triangles equal in all respects, be it corresponding sides or angles) back to back.
 Sides : Opposite sides are equal and parallel.
 Angles : Opposite angles are equal and adjacent angles are supplementary (which means adjacent angles add up to give 180 degrees).
 Diagonals : Diagonals are not equal but they bisect each other ( they themselves divide into two equal halves at the point they meet).
Rectangle
A rectangle can be considered as a parallelogram whose all four angles are equal. So when we adjust all the angles of a parallelogram to be 90 degrees each, we get a rectangle.
 Sides : Opposite sides are equal and parallel (no change when compared to a parallelogram)
 Angles : All angles are equal and each is equal to 90 degrees
 Diagonals : Diagonals are equal and bisect each other (diagonals can be obtained using Pythagoras theorem just because each angle is 90 degrees)
Rhombus
A rhombus is a parallelogram whose all four sides are equal. So just being a parallelogram, it is clear that all four angles are not necessarily equal but this obeys all the properties of a parallelogram. Let us see what are the additional properties.
 Sides : All sides are equal (it looks like two congruent isosceles triangles connected back to back).
 Angles : Opposite angles are equal and adjacent angles are supplementary (just as in case of a parallelogram).
 Diagonals : Diagonals bisect each other at 90 degrees (diagonals are not equal because each angle is not 90 degrees).
Square
A square is the one which follows all the properties discussed so far at its extremities.
 Sides : All sides are equal.
 Angles : All angles are equal.
 Diagonals : Diagonals are equal, they bisect each other at 90 degrees.
Trapezium
A trapezium is different from the quadrilaterals discussed above because it doesn't have much specifications to be achieved. The only condition to form a trapezium is that it should have one pair of opposite sides being parallel.
When trapeziums are considered and perpendiculars are dropped from the top vertices just as shown in the figure above, the quadrilateral formed within the intersection would be a rectangle but the right triangles on either side of this rectangle need not be congruent as their bases need not be the same always.
When the nonparallel sides of a trapezium are equal, then the right triangle formed would be congruent and hence would have the same base. This in turn gives the trapezium a new name : Isosceles trapezium.
In an isosceles trapezium,
 Nonparallel sides are equal.
 Base angles are equal.
 Diagonals are equal.
Isosceles Trapezium
Kite
A kite is a quadrilateral obtained by connecting two different isosceles triangles back to back.
 Sides : Adjacent sides of a kite are equal as shown in the above figure.
 Angles : One pair of opposite angles are equal.
 Diagonals : Diagonals intersect at 90 degrees and one of the diagonals get bisected.
Summary of Properties of Quadrilaterals
Type of Quadrilateral
 Sides
 Angles
 Diagonals


Parallelogram
 Opposite sides equal and parallel
 Opposite angles equal; Adjacent angles supplementary
 Diagonals bisect each other

Rectangle
 Opposite sides equal and parallel
 All angles equal
 Diagonals equal and bisect each other

Rhombus
 All sides equal and opposite sides parallel
 Opposite angles equal; Adjacent angles supplementary
 Diagonals bisect each other at right angles

Square
 All sides equal and opposite sides parallel
 All angles equal
 Diagonals equal and bisect each other at right angles

Trapezium
 One pair of opposite sides parallel
 Adjacent angles along nonparallel sides supplementary
 Diagonals not equal

Isosceles Trapezium
 One pair of opposite sides parallel and nonparallel sides equal
 Base angles equal
 Diagonals equal

Kite
 Adjacent sides are equal
 One pair of opposite angles are equal
 Diagonals intersect at 90 degrees and one diagonal gets bisected

Conclusion
We have seen how we could relate rectangles, rhombuses and squares to the basic figure parallelograms and have also discussed the addon properties which make them different from parallelograms in one way or the other. So it is always good to learn the properties of parallelograms and memorize the fact that rectangles are parallelograms with equal angles, rhombuses are ones with equal sides and squares are a combination of all of these. We also discussed about trapeziums and kites which stand away from this group as well. Now just try to recollect the properties, hope you would find it even more easier.
This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.
© 2019 Heera
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