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**14. Practical Geometry**

**Basic Constructions:**

Ruler, Compass, Divider, Set squares, Protractor.

**The tools in our geometry box are:****â€¢ **Ruler**â€¢ **Compass**â€¢ **Divider**â€¢ **Set squares**â€¢ **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:**

**â€¢ **Measuring lengths of line segments.**â€¢ **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:

**â€¢ **Marking off equal lengths.**â€¢ **Drawing arcs.**â€¢ **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:**

**â€¢ **Comparing lengths of line segments.**â€¢ **Helping avoid positioning errors.**â€¢ **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 **45Â° each**. The other set square is a scalene triangle with two angles measuring **30 Â°and 60Â°** each. The two perpendicular sides of either set square are graduated into centimetres.

**The basic uses of set squares are:**

**â€¢ **Drawing perpendicular lines.**â€¢ **Drawing parallel lines.

**Protractor:**

A **semi-circular too**l 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:**

**â€¢ **Measuring angles.**â€¢ **Drawing angles.

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

**â€¢ **Draw smooth and thin lines.**â€¢ **Mark points lightly.**â€¢ **Maintain tools or instruments with sharp pointers and fine edges.**â€¢ **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 i**s 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:****â€¢ **Draw a line AB.**â€¢ **Mark any point O on AB.

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**â€¢ **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.**â€¢ **Without changing the compass settings, draw an arc on line AB from point O. It cuts line AB at P.**â€¢ **Set the compass to length EF.**â€¢ **Without changing the compass settings, draw an arc from P cutting the previous arc at point Q.**â€¢ **Join points O and Q.**â€¢ **Hence, âˆ POQ is the required copy of âˆ 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 âˆ 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 âˆ LMN

**In a similar way, we can construct:****â€¢ **A 60Â° angle without using the protractor.**â€¢ **A 120Â° angle without using the protractor.**â€¢ **A 90Â° angle without using the protractor.

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