__Properties of parallelogram :__A

**quadrilateral**is a closed figure formed by four line segments and

A

**parallelogram**is a quadrilateral in which the opposite sides are parallel to each other.

**Property 1:**In a parallelogram, the opposite sides are of equal length

**Property 2:**In a parallelogram, the opposite angles are of equal measure

**Property 3:**The diagonals of a parallelogram bisect each other.

**Property 4:**If the opposite sides of a quadrilateral are of equal length, then the quadrilateral is a parallelogram.

**Property 5:**If the opposite angles in a quadrilateral are of equal measure, then the quadrilateral is a

parallelogram.

**Property 6:**If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

**Theorem 12:**A quadrilateral is a parallelogram if one pair of opposite sides are parallel and equal.

**Property 7:**If there are three or more parallel lines and the intercepts made by them on a transversal are

equal, then the corresponding intercepts on any other transversal are also equal

**Property 8:**In a triangle, the line joining the mid points of two sides is parallel to the third side and is equal

to one half of it.

**Property 9:**In a triangle, the line drawn through the mid-point of one side, parallel to another side, bisects the

third side.

**Theorem 13:**The medians of a triangle are concurrent and the point of concurrency divides each median in

the radio 2:1.

**Theorem 14:**Parallelograms on the same base and between the same parallels are equal in area.

**Theorem 15:**Triangles on the same base and between the same parallels are equal in area.

**Theorem 16:**If

a ray stands on a line, then the sum of the adjacent angles so formed is 180°.

**Theorem 17:**If two lines intersect, then the vertically opposite angles are of equal measure.

**Theorem 18:**The sum of the three angles of a triangle is 180°.

**Theorem 19:**The angles opposite to equal sides of a triangle are equal.

**Theorem 20:**The side opposite to the larger of two angles in a triangle is longer than the side opposite to the

smaller angle.

**Theorem 21:**A parallelogram is a rhombus if its diagonals are perpendicular.

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