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A Quadrilateral is an enclosed 4 sided figure which has 4vertices and 4 angles.There are two types of quadrilaterals and they are:- Convex quadrilateral:-A quadrilateral whose all four angles sum upto 360 degreeand diagonals intersect interior to it Concave quadrilateral:-A quadrilateral whose sum of four angles is more than 360degrees and diagonals intersect interior to it. There are many types of quadrilaterals which have many different properties.
A quadrilateral with opposite sides parallel andequal is a parallelogram .Properties:-• A diagonal of a parallelogram divides it intotwo congruent triangles.•In a parallelogram, opposite sides are equal.•In a parallelogram opposite angles are equal.•The diagonals of a parallelogram bisect eachother.These properties have their converse also.
A rectangle is a parallelogram with one angle 90 degreeThe properties of rectangle are:-The diagonals of rectangle are of equal length.It has including properties of parallelogram.It has two pairs of opposite sides equal.The opposite sides of rectangle are parallel to each other.
A square is a rectangle with adjacent sidesequal. The properties of a square are:-Square has including properties ofRectangleDiagonals of asquare bisect each other at 90Degrees and are equal.The all four interior angles of square areright angles.
A Rhombus is a parallelogram with adjacentsides equal. The properties of rhombus are:-A rhombus has the including properties ofA parallelogram.The diagonals of rhombus bisect each other at 90 degreeThe diagonals of rhombus bisect opposite angles
A trapezium is quadrilateral with one pair of opposite sides parallel andother sides are non parallelPROPERTIES OF TRAPEZIUM ARE:-Co-interior angles of parallel sides of trapezium are supplementarySum of the angles of trapezium are 360 degree.
A quadrilateral with two pairs of adjacent sidesequal is known as a kite. Properties of kite are:-The diagonals of a kite bisect each other 90degree.Adjacent sides of a kite are equal.The smaller diagonal bisect the angles of kite.Sum of angles of kite is 360 degree.
The line segment joining the mid point of twosides of a triangle is always parallel to thethird side and half of it.
Given:-D and E are the mid points of the sides ABand AC .To prove:-DE is parallel to BC and DE is half ofBC.construction:- Construct a line parallel to ABthrough C.proof:-in triangle ADE and triangle CFE AE=CE angle DAE= angle FCE (alternate angles ) angle AED= angle FEC (vertically opposite
Hence by CPCT AD= CF- - - - - - - - -1ButAD = BD(GIVEN)so from (1), we get,BD = CFBD is parallel to CFTherefore BDFC is a parallelogramThat is:- DF is parallel to BC and DF= BCSince E is the mid point of DFDE= half of BC, and , DE is parallel to BCHence proved .
According to the converse of mid point theoremthe line drawn through the mid point of one sideof a triangle, is parallel to another side bisects thethird side. WE CAN PROVE THE CONVERSE OF THE MID POINT THEOROM THROUGH THE EXPLANATION IN THE NEXT SLIDE .