Chapter 5.4, Problem 5WE

To determine

To mark: the appropriate features of the given quadrilaterals in the table.

Explanation of Solution

Given Information: A feature of a quadrilateral and four types of quadrilaterals.

The four basic quadrilaterals are considered here which are Parallelogram, Rectangle, Rhombus and Square. The given feature is that, a diagonal of the quadrilateral bisect each other.

A parallelogram is a quadrilateral in which, the diagonals divide themselves into two equal segments about their point of intersection.

  

In the above parallelogram, this feature can be expressed as,

  $\begin{array}{l}\overline{OQ}\cong \overline{OS}\\ \overline{OR}\cong \overline{OT}\end{array}$

Now, the remaining quadrilaterals which are rectangle, rhombus and square are parallelograms with their own specific features. and they satisfy all the properties of the parallelogram.

Thus, the feature is valid for all the quadrilaterals as marked below.

Property	Parallelogram	Rectangle	Rhombus	Square
Diags bisect each other	✔	✔	✔	✔