Identify quadrilaterals

A quadrilateral is a closed, two-dimensional polygon with exactly four straight sides, four vertices, and four angles; it may vary in size, orientation, and side lengths. Identification depends on these defining attributes rather than appearance, so squares, rectangles, rhombi, trapezoids, and irregular four-sided figures can all qualify, while open shapes or figures with curved sides do not; formal angle measurement and proofs are beyond this understanding.

Detailed Explanation: Identify quadrilaterals

A quadrilateral is a closed shape with exactly four straight sides. It also has four corners, called vertices, and four angles.

To identify one, check:

Is the shape closed?
Are all its sides straight?
Does it have exactly four sides?

Worked example

Suppose a shape has points $A$ , $B$ , $C$ , and $D$ . Its sides are:

$\overline{AB}$
$\overline{BC}$
$\overline{CD}$
$\overline{DA}$

Check the shape:

It is closed because the last side, $\overline{DA}$ , connects back to the starting point $A$ .
All four sides are straight.
It has exactly four sides and four corners.

Therefore, the shape is a quadrilateral. It does not matter whether it is tilted, has equal sides, or looks unusual. What matters is that it is closed and has exactly four straight sides.

Learn by doing: Identify quadrilaterals

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Classifying Polygons by Sides

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