Chapter Notes: Practical Geometry

# Practical Geometry Class 6 Notes Maths

14. Practical Geometry

Basic Constructions:

Ruler, Compass, Divider, Set squares, Protractor.

The tools in our geometry box are:
• Ruler
• Compass
• Divider
• Set squares
• Protractor

The description of each tool and its uses are given below:

Ruler:
A ruler is a flat and straight-edged strip, whose one side is graduated into centimetres and the other into inches. A ruler is commonly called a scale. It is the most essential tool in geometry. It is used in all constructions.

The basic uses of a ruler are:

• Measuring lengths of line segments.
• Drawing line segments.

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Compass:

A compass has two ends. One end holds a pointer, while the other end holds a pencil. It is also called a pair of compasses.
The basic uses of a compass are:

• Marking off equal lengths.
• Drawing arcs.
• Drawing circles.

Divider:

A divider is a tool similar in shape to a compass. It has a pair of pointer ends.

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The basic uses of a divider are:

• Comparing lengths of line segments.
• Helping avoid positioning errors.
• Taking accurate measurements.

Set squares:

The two triangular tools in the geometry box are called set squares. One of the set square is an isosceles triangle with two angles measuring 45° each. The other set square is a scalene triangle with two angles measuring 30 °and 60° each. The two perpendicular sides of either set square are graduated into centimetres.

The basic uses of set squares are:

• Drawing perpendicular lines.
• Drawing parallel lines.

Protractor:

A semi-circular tool with degrees marked is called a protractor. The centre of the semicircle is called the midpoint of the protractor. This point helps as a reference point for the protractor. The horizontal line is called the base line or the straight edge of the protractor.

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The basic uses of a protractor are:

• Measuring angles.
• Drawing angles.

The important points to be remembered while using the tools for construction are:

• Draw smooth and thin lines.
• Mark points lightly.
• Maintain tools or instruments with sharp pointers and fine edges.
• Keep two pencils in the box. One is for drawing lines and marking points. The other is for using in the compass.

Construction of Lines:

Steps to construct a line segment of length 5 cm

Steps to construct a line segment of length 5 cm:

 Draw line 1. Mark a point on line l and name it P. Open the compass to measure the length of the line segment by placing the pointer on the 0 mark of the ruler and the pencil point on the 5 cm mark. Place tlie pointer of the compass on point P. Swing an arc oil tlie line to cut it at Q. is the required line segment of length 5 cm.

Two lines are said to be perpendicular when they intersect each other at an angle of 90o.

The perpendicular bisector is a perpendicular line that bisects another line into two equal parts.

Constructing of Angles

An exact copy of a line segment can be constructed using a ruler and a compass.

An exact copy of a line segment can be constructed using a ruler and a compass.

To construct a copy of an angle:
• Draw a line AB.
• Mark any point O on AB.

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• Place the compass pointer at vertex X of the given figure and draw an arc with a convenient radius, cutting rays XY and XZ at points E and F, respectively.
• Without changing the compass settings, draw an arc on line AB from point O. It cuts line AB at P.
• Set the compass to length EF.
• Without changing the compass settings, draw an arc from P cutting the previous arc at point Q.
• Join points O and Q.
• Hence, ∠POQ is the required copy of ∠YXZ

To construct the bisector of an angle:

Let the given angle be LMN.
Place the compass pointer at vertex M of the given angle.

Draw an arc cutting rays ML and MN at U and V, respectively.

Draw an arc with V as the centre and a radius more than half the length of UV in the interior of ∠LMN.

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Draw another arc with U as the centre and the same radius intersecting the previous arc.

Name the point of intersection of the arcs as X.

Join points M and X.

Thus, the ray MX is the required bisector of ∠LMN

In a similar way, we can construct:
• A 60° angle without using the protractor.
• A 120° angle without using the protractor.
• A 90° angle without using the protractor.

The document Practical Geometry Class 6 Notes Maths is a part of the Class 6 Course Mathematics (Maths) Class 6.
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## Mathematics (Maths) Class 6

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## FAQs on Practical Geometry Class 6 Notes Maths

 1. What is practical geometry?
Ans. Practical geometry is a branch of mathematics that deals with the study of geometric shapes and their properties in real-world applications. It involves using tools such as a ruler, compass, protractor, and other measuring instruments to construct and solve problems related to lines, angles, triangles, quadrilaterals, and other geometric figures.
 2. What are the basic tools used in practical geometry?
Ans. The basic tools used in practical geometry include a ruler, compass, protractor, pencil, eraser, and a pair of dividers. These tools help in measuring and constructing various geometric shapes accurately.
 3. How can I construct a right angle using a compass and ruler?
Ans. To construct a right angle using a compass and ruler, follow these steps: 1. Draw a line segment using a ruler. 2. Place the compass at one end of the line segment and draw an arc that intersects the line. 3. Without changing the compass width, place the compass at the other end of the line segment and draw another arc that intersects the line. 4. Using a ruler, draw a line connecting the two points where the arcs intersect the line segment. The angle formed at the intersection is a right angle.
 4. How can I construct a perpendicular bisector of a line segment?
Ans. To construct a perpendicular bisector of a line segment using a compass and ruler, follow these steps: 1. Draw a line segment using a ruler. 2. Place the compass at one end of the line segment and draw an arc that intersects the line. 3. Without changing the compass width, place the compass at the other end of the line segment and draw another arc that intersects the line. 4. Using a ruler, draw a straight line connecting the two points where the arcs intersect. This line will be the perpendicular bisector of the given line segment.
 5. How can I construct an equilateral triangle using a compass and ruler?
Ans. To construct an equilateral triangle using a compass and ruler, follow these steps: 1. Draw a line segment using a ruler. 2. Place the compass at one end of the line segment and draw an arc. 3. Without changing the compass width, place the compass at the other end of the line segment and draw another arc that intersects the previous arc. 4. Using a ruler, draw a straight line connecting the two points where the arcs intersect. This line will be the base of the equilateral triangle. 5. With the same compass width, place the compass at one of the endpoints of the base and draw an arc that intersects the base. 6. Repeat step 5 with the other endpoint of the base. 7. Using a ruler, draw lines connecting the endpoints of the base with the intersections on the base. The resulting figure will be an equilateral triangle.

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