Question

A photo frame is in the shape of a quadrilateral with one diagonal longer than the other. Name the quadrilateral and justify your answer.

Answer 1

Hint:
Quad means four! If an area is enclosed by 4 sides then we’ll say it’s a quadrilateral. Quadrilaterals can be divided into different sub-parts depending upon angles and sides. That’s what we’ll use here. We have to find quadrilaterals with diagonals of different lengths.

Complete step by step solution:
There are many shapes in geometry that are having diagonals. Square, rectangle, parallelogram, rhombus etc. But the condition of the photo frame is the diagonals should be different in length. Diagonals of square and rectangle are equal in length. thus they are not our answer. In case of parallelogram also the diagonals bisect each other. Thus only it is the rhombus that has diagonals of different length. They can be equal only if all four sides are of the same length that forms a square. So, the quadrilateral is a RHOMBUS.

Note:
Additional information:

Name of the shape	Nature of sides	Nature of diagonals
Square	Have 4 sides.All are of the same length.	Have 2 diagonals.They are congruent to each other.
rectangle	Have 4 sides.Opposite sides are of the same length.	Have 2 diagonals.Both are congruent to each other.
parallelogram	Have 4 sides.Opposite sides are parallel to each other.	Have 2 diagonals.They are perpendicular bisectors of each other.
rhombus	Have 4 sides.All sides are congruent.Opposite sides are parallel.	Have 2 diagonals.They are perpendicular bisectors of each other.