Question

write all the properties of parallelograms. trapeziums and kite

Answer 1

Hey friend here is your answer

Trapezium = trapezium is a quadrilateral with one pair of opposite side parallel.
-The parallel sides are called bases and non parallel sides are called legs.
-If two non parallel sides are equal and angles are also equal than that is an isoceles trapezium.

Kite = A kite is a quadrilateral that has 2 pairs of equal length sides and these sides are adjacent to each other.
-Two angles are equal where two unequal sides meet.
-A kite is symmetrical at its main diagonal.
-The shorter diagonal divides kite into two isocels triangle.

Parallelogram = It is a quadrilateral with two pairs parallel .
- Opposite sides are parallel and equal in length.
- Opposite angles are equal.
-it has two diagonal intersect at each other .
-Two diagonals divide it into four triangles.
- Square , rectangle and rhombus are special type of parallelograms.

Hope it will help you.

Answer 2

Trapezium:

A trapezium is a quadrilateral with exactly one pair of parallel sides.

Remember, a trapezium has only one pair of opposite sides to be parallel which clearly says it is not a parallelogram.


The parallel sides of a trapezium are also called bases and the other two non-parallel sides are called legs.

If the two non-parallel sides are equal and form equal angles at one of the bases, the trapezium is called an isosceles trapezium.

Now, let’s see some properties of a trapezium.

Properties of a Trapezium:

A trapezium has exactly one pair of parallel sides.

A line segment joining midpoints of non-parallel sides is parallel to the parallel sides.

A line segment joining midpoints of the parallel side is half the sum of the lengths of its parallel sides i.e. mid-segment = 1/2(base1 + base2).

If a trapezoid is having sides a, b, c, and d and diagonals p and q, the following equation holds true- p2+q2=c2+d2+2ab.

This was all about trapezium which you need to know in brief. Now, let’s learn about another type of quadrilateral falling into this category.

Kite:

A kite is a quadrilateral with exactly two pairs of the equal consecutive side or in which two disjoint pairs of consecutive sides are congruent (disjoint pairs means that one side can’t be used in both pairs).

The area of a kite is half the product of its diagonals. Area of Kite = (d1*d2)/2 where d1 and d2 are the lengths of the diagonals.

You need to know that every Rhombus is a kite, as Rhombus satisfies all the properties of a kite. A kite with opposite sides parallel definitely becomes a rhombus. Thus every Rhombus is a Kite but not vice versa.

Also, remember this doesn’t mean that a kite is also a parallelogram. A kite is not a parallelogram according to its properties.

Now, let’s look at some of the properties of a Kite.

Properties of a Kite:

The diagonals of a kite are perpendicular to each other.

The diagonals of a kite bisect each other.

The main diagonal bisects a pair of opposite angles.

The shorter diagonal divides the kite into two isosceles triangles.

There are six important properties of parallelograms to know:

Opposite sides are congruent (AB = DC).

Opposite angels are congruent (D = B).

Consecutive angles are supplementary (A + D = 180°).

If one angle is right, then all angles are right.

The diagonals of a parallelogram bisect each other.