Perpendicular Lines

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.

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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.

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