##
**Perpendicular Lines**

Two line segments are said to be perpendicular lines if the
angle between them is 90°.

In the given figure, ∠ACD = ∠BCD = 90°, so the line segments AB and CD are perpendicular. It is
written as AB⊥CD and read as AB perpendicular to CD or vice-versa.

###
**Construction of a perpendicular line using a set square**

To construct a perpendicular line to a given line, we follow
the following steps:

**Step 1:**Draw a line PQ of the given measurement and take a point M.

**Step 2:**Hold the ruler firmly along the line PQ.

**Step 3:**Place a set square with its shortest side against the ruler at M.

**Step 4:**Slide the set square firmly till the perpendicular edge is on the point M.

**Step 5:**Draw a line MN along the perpendicular edge of the set square. Then MN is the perpendicular to PQ at M.

###
**Construction of a perpendicular from a point by using a compass**

To construct a perpendicular by using compass, we follow the
following steps:

**Step 1:**Draw a line segment AB and take any point C above AB.

**Step 2:**Draw an arc PQ on the line segment AB from the point C.

**Step 3:**Draw arcs from the points P and Q below AB so that two arcs intersect and join the point C and intersection point or arcs.

∴
CD is perpendicular to AB i.e.CD⊥AB.

###
**Construction of a perpendicular at a point of the given line by using
a compass**

To construct a perpendicular at a point of the given line by
using a using a compass, we follow the following steps:

**Step 1:**Draw a line segment AB. Take any point C on the line segment AB.

**Step 2:**Fix the compass needle at point C and draw an arc at C and level one point M as shown in the figure. Without changing the span of the compass, cut two arcs from point M and level it putting the compass needle at M to P and from P and level it Q.

**Step 3:**Putting the needle of the compass at P and Q, draw two arcs so that they intersect at D as shown in the figure. Join the points C and D.

∴
CD is perpendicular to AB i.e.CD⊥AB.

*You can comment your questions or problems regarding the perpendicular lines here.*

## 0 comments: