Constructing Squares and Rectangles

Constructing a Square

Task: Construct a square $PQRS$ with a side length of 6 cm.

Method: Ruler and Compass

Step 1: Draw a line segment $PQ$ of length 6 cm.

Step 2: At point $P$, construct a perpendicular line (90°).

• You can do this using a set square or a protractor, or by compass construction (bisecting a straight angle).
• Let this vertical line be the “ray” from $P$.

Step 3: Mark the length.

• Set your compass radius to 6 cm.
• Place the needle on $P$ and cut an arc on the vertical line.
• Mark this intersection point as $S$. Now $PS = 6$ cm.

Step 4: Find point $R$.

• We know $QR = 6$ cm and $SR = 6$ cm.
• With center $Q$ and radius 6 cm, draw an arc.
• With center $S$ and radius 6 cm, draw another arc.
• The point where these two arcs intersect is $R$.

Step 5: Join $Q$ to $R$ and $S$ to $R$.