# Constructing a square

### Objectives

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

40 minutes

### 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)

1. To construct a square of a given length, draw a line segment AB of given length.
2. Draw perpendicular to the line AB at A.
3. Taking AB as radius draw a circle with A as centre.
4. The circle intersects the perpendicular at a point. Name the intersecting point as C.
5. Similarly draw perpendiculars to AC at C. You get third side of the square.
6. To get the fourth side of the square construct a perpendicular to AB at B.
7. Name the two intersecting perpendiculars as D.
8. ABCD would be the required square.
• Developmental Questions:
1. For what measure are you drawing a square ?
2. What is a perpendicular line ?
3. Why are we constructing perpendicular lines for constructing a square ?
4. What is the purpose of drawing a circle ?
5. How do we determine the fourth vertex of the square ?
• Evaluation:
1. What are perpendicular lines ?
2. Why is a circle being drawn ? Which purpose would it solve ?
• Question Corner
1. Can a square be constructed without using a compass ?