Question

Which basic property of a square will you use, if you are asked to draw a square with diagonal measuring 5 cm?

Answer 1

The property that angle between a side and a diagonal of a square is ${45}^{\circ }$ will be used in this construction.

Step 1: Draw a horizontal line AB of any length

Step 2: At A, construct an angle of ${45}^{\circ }$ and cut a line segment of 5 cm as the diagonal and mark the point as P.

Step 3: Draw the perpendicular bisector of AP and let it meet at O.

Step 4: With O as centre and radius equal to 2.5 cm, draw arcs above and below to cut the perpendicular bisector at X and Y.

Step 5: Join AX, AY , PX and PY to obtain the square.

So, the angle between a side and a diagonal of a square is ${45}^{\circ }$