Chapter 6.4, Problem 37PPS

To determine

To explain:

The construction steps to form a rectangle through the construction of congruent segments and line perpendicular to another line through a point on the line

Answer to Problem 37PPS

The rectangle is formed through the construction of congruent segments and line perpendicular to another line through a point on the line as:

  

Explanation of Solution

Step 1:

First graph a straight line in the coordinate plane. Place the points $\mathrm{P}$ and $\mathrm{Q}$ on the line.

Step 2:

Need to draw an arc on both sides left and right side of the point $\mathrm{P}$ by placing the compass at the point $\mathrm{P}$ that intersects.

Step 3:

Open the compass to a setting greater than the distance from $\mathrm{P}$ to either point of intersection.

Then draw an intersecting curves curve by placing a compass at point of intersection above $\overleftrightarrow{\mathrm{P}\mathrm{Q}}$ .

Step 4:

Through point $\mathrm{P}$ draw a line $\mathrm{a}$ . Use the step 3 to draw arcs

Step 5:

Use the point $\mathrm{Q}$ by repeating step 2 and 3

Step 6:

Through point $\mathrm{Q}$ draw a line $\mathrm{b}$ . Use the step 5 to draw the intersection arcs

Step 7:

Draw an arc above point $\mathrm{P}$ which intersects line $\mathrm{a}$ by placing a compass at point $\mathrm{P}$ . Give name point $\mathrm{R}$ to this new point intersection.

Step 8:

Use the same setting, you need to put your compass at point $\mathrm{Q}$ and draw an arc. Give name point $\mathrm{S}$ to this new point intersection.

Check the following rectangle which is formed by using above all steps: