Question

The points P and Q in the following figure define the line segment (PQ⎯⎯⎯⎯⎯) P Q . The steps involved in using a compass to construct the perpendicular bisector of the line segment (dashed line) are listed in random order below. In the spaces provided, list the letters associated with each step, in the correct, logical order to construct the perpendicular bisector of PQ⎯⎯⎯⎯⎯ P Q .

Answer 1

You haven't provided the steps.

mathisfun.com/geometry/construct-linebisect.html

Here is a useful link to the correct steps. The instructions may not be exactly the same but I think you can do it.

Answer 2

Using P and Q as centers, draw arcs on both sides of PQ with radii exceeding half its length. Connect intersecting points R and S, forming RS. With PR=QR=4 cm, RS is the perpendicular bisector of PQ.

To construct the perpendicular bisector of line segment PQ, initiate the process by using P and Q as centers and drawing arcs on both sides of PQ with radii greater than half the length of PQ.

The intersection points of these arcs, denoted as R and S, are connected to form line segment RS. Remarkably, RS equals PQ, and the angle ∠POR is precisely 90 degrees, demonstrating the perpendicularity of RS to PQ.

This implies that RS serves as the perpendicular bisector of PQ, cutting it at P and forming right angles.

Measurement reveals that PR and QR both extend to 4 cm, signifying their equality. In essence, the construction successfully achieves a perpendicular bisector with equal segments PR and QR, each measuring 4 cm.

Question:-

Draw a line segment PQ= 8 cm. Construct the perpendicular bisector of the line segment PQ. Let the perpendicular bisector drawn meets PQ at point R. Measure the length of PR and QR. Is PR=QR?