# Constructing a square

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### Objectives

- Construction of a perfect square.
- Use of equal radius arcs to get equal sides of a square in the construction protocol.
- Use of perpendicular lines to draw sides of a square.

### Estimated Time

40 minutes

### Prerequisites/Instructions, prior preparations, if any

### Materials/ Resources needed

Non digital: White paper, compass, pencil and scale.

This activity has been taken from the website :http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Mylod/Math7200/Project/Square.html

- Process:

### Process (How to do the activity)

- To construct a square of a given length, draw a line segment AB of given length.
- Draw perpendicular to the line AB at A.
- Taking AB as radius draw a circle with A as centre.
- The circle intersects the perpendicular at a point. Name the intersecting point as C.
- Similarly draw perpendiculars to AC at C. You get third side of the square.
- To get the fourth side of the square construct a perpendicular to AB at B.
- Name the two intersecting perpendiculars as D.
- ABCD would be the required square.

- Developmental Questions:

- For what measure are you drawing a square ?
- What is a perpendicular line ?
- Why are we constructing perpendicular lines for constructing a square ?
- What is the purpose of drawing a circle ?
- How do we determine the fourth vertex of the square ?

- Evaluation:

- What are perpendicular lines ?
- Why is a circle being drawn ? Which purpose would it solve ?

- Question Corner

- Can a square be constructed without using a compass ?