Question

Diagonals in following quadrilateral are equal or

I) parallelogram. 2) rhombus 3) rectangle 4) trapezium

Answer 1

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1) Same

A simple (non-self-intersecting) quadrilateral is aparallelogram if and only if any one of the following statements is true: Two pairs of opposite sides areequal in length. Two pairs of opposite angles areequal in measure. The diagonals bisect each other




2) A rhombus is a type of parallelogram, and what distinguishes its shape is that all four of its sides are congruent.

Diagonals are perpendicular..

• AOD = 90°
• AOB = 90°
• BOC = 90°
• COD = 90°

The diagonals of a rhombus bisect each other. This means that they cut each other in half.

• Therefore, diagonals being equal is a special case when all the sides of the rhombus are equal i.e it is a square. Otherwise not.

3) The two diagonals are equal in length and bisect each other. Every quadrilateral with both these properties is a rectangle. A rectangle is rectilinear: its sides meet at right angles.





4) Only if the trapezium is regular, in whch case it is symmetric and hence the diagonals are symmetric and equal in length

It is a special case of a trapezoid. ... In any isoscelestrapezoid two opposite sides (the bases) are parallel, and the two other sides (the legs) are of equal length (properties shared with the parallelogram). Thediagonals are also of equal length.