Question

Describe how you would construct each of the following:

The square whose sides each have length$AC$.

Short answer

The construction of a square with side length equal to $\overline{AC}$

Step-by-step solution

Step 1. Given information.   

The given statement is “a square with side length equal to $\overline{AC}$”.

Step 2. Concept used.

Taking side $\overline{AC}$ as side of square.

Step 3. Solution.

The procedure to construct of square:

• Consider the line segment $\overline{AC}$.and extend it.

• Using $C$as centre draw two arcs of same radii that intersects the line $\overline{AC}$at two

Points $X \&Y$.

• As $X \&Y$as centers with suitable radius draw two arcs that intersect at point$Z$.

• Draw the line $\overline{CZ}$and extend it.

• Using the length of$\overline{AC}$with center $C$,draw an arc on the line $\overline{CZ}$. Label the

point $E$.

• Using the length of $\overline{AC}$with center $A$,draw an arc on the line $\overline{CZ}$. Label the

point $F$.

• Join $\overline{EF}$and $\overline{AF}$.

The construction is shown below.

Hence, the construction of a square with side length equal to$\overline{AC}$