Chapter 5.4, Problem 2WE

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 forms two congruent triangles.

A quadrilateral with its opposite sides being parallel to each other and congruent is referred to as a “parallelogram”.

  

The figure shown above represents a parallelogram with,

  $\begin{array}{l}\overline{EF}\cong \overline{GH}\\ \overline{EH}\cong \overline{GF}\end{array}$

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
Opp sides are $\cong$	✔	✔	✔	✔