In Geometry, to measure the height of figures, we use perpendicular lines. Using a set square, find the height of the given figures.

**Construction
of Perpendicular Lines**

__1.
Introduction__

Have you ever noticed that the wall and floor are
always perpendicular to each other? So, to measure our heights, we make use of scale
represented on the walls as shown in the figure.

In Geometry, to measure the height of figures, we
use perpendicular lines. Using a set square, find the height of the given figures.

Let us learn to construct perpendicular lines by
using set square.

__ __

__2.
Set Squares__

The set squares are two triangle shaped instruments
in the Geometry Box. Each of them has a right angle. One set square has the angles 30°, 60°, 90° and the other
set square has the angles 45°, 45°, 90°. The perpendicular edges are graduated in
centimetres.

**Set squares have several uses:**

• To construct the specific angles 30° , 45° , 60°
, 90°

• To draw parallel and perpendicular lines

• To measure the height of the shapes

If the perpendicular from P meets
AB at Q, the point Q is called the foot of the perpendicular from P to AB and the
symbol " ⊥" means “is perpendicular to”.
i.e., PQ ⊥
AB

__Example 5: __

Construct a line perpendicular to the given line at a point on the line.

**Step 1: **Draw a line AB and take a point P anywhere on the line.

**Step 2: **Place the set square on the line** **in such a way that the vertex which
forms right angle coincides with P and one arm of the right angle coincides with
the line AB.

**Step 3: **Draw a line PQ through P along** **the other arm of the right angle of
the set square.

**Step 4: **The line PQ is perpendicular to the** **line AB at P. That is, PQ ⊥ AB and ∠APQ = ∠BPQ
= 90° .

__Example 6: __

Construct a line perpendicular to the
given line through a point above it.

**Step 1: **Draw a line PQ. Take a point X anywhere
above the line PQ.

**Step 2: **Place one of the arms of the right** **angle of a set square along the line
PQ and the other arm of its right angle touches the point X.

**Step 3: **Draw a line through the point** **meeting PQ at Y.

**Step 4: **The line XY is perpendicular to the** **line PQ at Y. That is, XY ⊥ PQ

Tags : Geometry | Term 2 Chapter 4 | 6th Maths , 6th Maths : Term 2 Unit 4 : Geometry

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6th Maths : Term 2 Unit 4 : Geometry : Construction of Perpendicular Lines | Geometry | Term 2 Chapter 4 | 6th Maths

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