Quadrilaterals

40. The Square's Signature · four equal sides, four perfect corners

Dragging A moves the square. It remains a perfect square with equal sides and right angles.

Drag corner A — the square resizes but always stays a perfect square: four equal sides and four right angles.

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Selina ICSE: Quadrilaterals

What this lesson covers

Try dragging point A. Watch how the square moves. Do the angles stay 90°? Do the sides stay equal?

Construct a square.

Place point A — the first corner of the square.
Place point B to set base AB. Keep it a moderate length, low and centred, so the square has room to grow upward into the open space.
Draw side AB (Segment tool: click A, then B).
With the Perp tool, click point A, then click in the open space ABOVE the base — it draws the line of side AD, square to AB at A.
With the Arc tool, click A for the centre, then click exactly on B — an arc of radius AB swings around A.
Mark point D where the arc crosses the perpendicular — D is exactly AB from A, so side AD equals AB and meets AB at 90°.
With the Perp tool, click point B, then click toward D — it draws the line of side BC, square to AB at B.
With the Arc tool, click once on B — the same-radius arc swings around B.
Mark point C where the arc from B crosses the perpendicular, on the same side as D — side BC equals AB.
Draw the last side DC (Segment tool: click D, then C). ABCD is a square — four equal sides, four right angles.

Prove that the figure has four equal sides and four right angles.

A square is defined as a quadrilateral with four sides of equal length.
A square is also defined by having four interior angles, each measuring exactly 90°.
Therefore, any quadrilateral satisfying both conditions (4 equal sides + 4 right angles) is a square.

Which of the following statements correctly defines a square?

A square is defined as a quadrilateral with all four sides equal in length and all four interior angles measuring exactly 90°.