Co-Authored By:

##### Asked by: Dwana Llovet

science space and astronomy# How do you construct a perpendicular line segment?

**Construct: a line through P perpendicular togivenline.**

- STEPS:
- Place your compass point on P and swing an arc of any sizethatcrosses the
**line**twice. - Place the compass point on one of the two locations wherethearc crossed the
**line**and make a small arc belowthe**line**(on the side where P is not located).

Also, how do you construct a perpendicular bisector of a segment?

**The perpendicular bisector of a line segment**

- open the compass more than half of the distance between A andB,and scribe arcs of the same radius centered at A and B.
- Call the two points where these two arcs meet C and D. Drawtheline between C and D.
- CD is the perpendicular bisector of the line segment AB.
- Proof.

**line segment**PQ that wewill

**copy**. Mark a point R that will be one endpoint of thenew

**line segment**. Set the compasses' point on the point P ofthe

**line segment**to be

**copied**. Adjust thecompasses'width to the point Q. The compasses' width is now equalto thelength of the

**line segment**PQ.

Additionally, how many perpendicular bisectors can be constructed for a line segment?

For every **line segment**, there isone**perpendicular bisector** that passes through themidpoint.There are infinitely **many bisectors**, but onlyone**perpendicular bisector** for any**segment**.

**Steps**

- Draw one of the lines and mark two points on it.
- Set a compass to at least half the distance between thetwopoints.
- Use the compass to draw a circle centered around each point.Thecircles should intersect in two points on opposite sides oftheline.
- Draw a line through the two points of intersection.