What is Square?
A square is a quadrilateral and a polygon with 4 vertices and 4 sides enclosing four angles, to note. 360 degrees is the sum of the interior angles. In general, a quadrilateral has sides of varying lengths and angles of different measurements. However, with some of their sides and angles being equal, triangles, rectangles, etc. are special kinds of quadrilaterals.
A square is a regular quadrilateral in geometry, which implies it has :
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Four equal sides.
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Four equal angles (90-degree angles, or 100-gradian angles or right angles).
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It can also be represented as a rectangle in which the length of two adjacent sides is equal.
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A square with ABCD vertices will be denoted as □ABCD.
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Constructing a Square With a Compass
Square in construction is quite easy to draw as it requires only a few steps which are very easy to implement. While we focus on the square for construction, we have to take care of the following properties:
Therefore, the following are the steps for the construction of square:
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Draw a reference line AB of 6cm using a ruler.
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Draw the 90 degree angle at A with the aid of the compass.
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Draw the 90 degree angle at B with the aid of the compass.
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Using an open compass 6 cm wide. Draw an arc with A as the centre; that cuts arms at a 90 degree angle. And mark the intersection point as C.
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Using the ruler find length measure of AC. The AC length should be 6 cm.
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Using the compass again and take 6 cm width of the compass. With D as the middle, draw an arc that cuts arms at an angle of 90 degrees. And mark the junction point as D.
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Using the ruler and the BD length measurement. The BD length should be 6 cm and we’ll get:
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Join CD.
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Use the CD ruler and calculate its length. CD should be 6 cm in length and we get the corresponding square ABCD.
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Constructing a Square in a Circle
The steps to inscribe a square in a circle are:
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Draw a circle using your compass and mark the middle O.
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Draw a circular diameter using your ruler, marking the endpoints A and B.
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Build the perpendicular diameter bisector, AB.
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Label the points where the circle is intersected by the bisector as C and D.
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For the square to form, link points A to B to C to D.
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Solved Examples
1. Construct a square with a side of length 7cm.
Solution:
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Draw a reference line AB of 7 cm using a ruler.
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Draw the 90 degree angle at A with the aid of the compass.
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Draw the 90 degree angle at B with the aid of the compass.
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Using an open compass 6 cm wide. Draw an arc with A as the centre; that cuts arms at a 90 degree angle. And mark the intersection point as C.
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Using the ruler find length measure of AC. The AC length should be 6 cm.
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Using the compass again and take 7 cm width of the compass. With D as the middle, draw an arc that cuts arms at an angle of 90 degrees. And mark the junction point as D.
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Using the ruler and the BD length measurement. The BD length should be 6 cm and
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Join CD.
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Use the CD ruler and calculate its length. The CD should be 7 cm in length and we get the corresponding square ABCD.
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2. Construct a circle with radius 5 cm and draw a square inside it.
Solution:
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Draw a circle with radius 5 cm using your compass and mark the middle O.
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Draw a circular diameter using your ruler, marking the endpoints A and B.
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Build the perpendicular diameter bisector, AB.
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Label the points where the circle is inters
ected by the bisector as C and D. -
For the square to form, link points A to B to C to D.
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Did You Know?
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A square is a regular quadrilateral since it has 4 sides of equal length.
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Often, a square is a rectangle with equal sides and a right-angled rhombus.
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A square’s area equals the length of one side to the power of two (length squared).