What is Special quadrilaterals? — Mathematics

Definition 41.3 Primary & Middle School Mathematics · Chapter 41 — Triangles and Quadrilaterals

A quadrilateral has four vertices and four sides. It is a:

rectangle when its four angles are right angles;
rhombus when its four sides have the same length;
square when it is both: four right angles and four equal sides.

The three special quadrilaterals with their diagonals (in red). The square inherits the properties of both the rectangle and the rhombus.

Examples

Example 41.6 (Recognizing a shape from its properties)

A quadrilateral has four sides of length $4$ cm and one right angle. What is it? Four equal sides make it a rhombus. In a rhombus, opposite angles are equal and the four angles add up to $360^\circ$ ; one right angle then forces all four to be right (this will be proved with parallelograms in Chapter 52). So the shape is a square.

Example 41.8

Program for a square $ABCD$ of side $4$ cm:

Draw a segment $[AB]$ with $AB = 4$ cm.
Draw the perpendicular to $(AB)$ at $A$ ; on it, place $D$ at $4$ cm from $A$ (choose one side of the line and stick to it).
Draw the perpendicular to $(AB)$ at $B$ ; on it, place $C$ at $4$ cm from $B$ , on the same side as $D$ .
Join $C$ and $D$ .

Check with the ruler: $DC$ should measure $4$ cm too.

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Examples

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