Mathematics, Quadrilaterals, Class IX

Quadrilaterals class 9

properties of parallogram

One special kind of polygons is called a parallelogram. It is a quadrilateral where both pairs of opposite sides are parallel.

Different types of quadrilaterals

There are six basic types of quadrilaterals. They are:

Trapezium

Parallelogram

Rectangle

Rhombus

Square

Kite

properties of sqaure

Square is a quadrilateral with four equal sides and angles. It's also a regular quadrilateral as both its sides and angles are equal. Just like a rectangle, a square has four angles of 90° each.

properties of rectangle

A rectangle is a parallelogram with four right angles. Rectangles are much simpler to deal with than the general case of a parallelogram.

properties of rhombus

A rhombus is a special case of a parallelogram and it is a four-sided quadrilateral. In a rhombus, opposite sides are parallel and opposite angles are equal.

Mid point theorem result

We conclude that the line joining the mid-point of two sides of a triangle is equal to half the length of the third side.

Converse of Mid point result

The converse of the midpoint theorem states that " if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side".

figures between the same paralllel lines

two figures are said to be on the same base and between the same parallels, if they have a common base (side) and the vertices (or the vertex) opposite to the common base of each figure lie on a line parallel to the base.

Axiom of area

(1) The area of a square with a side of length one unit is defined to be one square unit. (2) Let a surface be divided into a finite number of smaller non-overlapping surfaces. ... Then the sum of the areas of the smaller surfaces equals the area of the larger surface. (3) Equal surfaces have equal areas.

Area of parallelogram

a parallelogram is a two-dimensional figure with four sides. It is a special case of the quadrilateral. The sum of the interior angles in a quadrilateral is 360 degrees.

Area of triangle

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.

when parallelogram becomes a rectangle

If a parallelogram is known to have one right angle, then repeated use of co-interior angles proves that all its angles are right angles. If one angle of a parallelogram is a right angle, then it is a rectangle

when parallelogram becomes a square

The only parallelogram that satisfies that description is a square. Theorem 16.8: If the diagonals of a parallelogram are congruent and perpendicular, the parallelogram is a square.

when parallelogram becomes a rhombus

If either diagonal of a parallelogram bisects two angles, then it's a rhombus (neither the reverse of the definition nor the converse of a property). If the diagonals of a parallelogram are perpendicular, then it's a rhombus

Difine all quadrilaterals

a quadrilateral is a polygon with four edges and four vertices. Sometimes, the term quadrangle is used, by analogy with triangle, and sometimes tetragon for consistency with pentagon and hexagon, or 4-gon for consistency with k-gons for arbitrary values of k.