Chapter 10.2, Problem 7CE

To determine

To describe: the construction of a square with side length equal to $AC.$ .

Explanation of Solution

Given information:

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

The procedure to construct of square:

• Consider the line segment $\overline{AC}$ .and extend it.
• Using Cas centre draw two arcs of same radii that intersects the line $\overline{AC}$ at two

pointsX and Y.

• As X and Yas 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 centerC, draw an arc on the line $\overline{CZ}$ . Label the

point $E.$ .

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

point $F$ .

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

The construction is shown below.

  

Hence, theconstruction of a square with side length equal to $AC.$