Construction / Practical Geometry (basics) : Construction of Line, Circle, Angle

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Construction of Line, Circle, Angle

what you'll learn...

overview

In this page, overview of construction of the following are provided

• a line segment

• a circle of given radius

• a semi circle of given radius

• a line by copying another line

• constructing an angle by copying another angle

Constructing a Line segment

To construct a line segment of length $6$ $6$ cm, the ruler is used.

Constructing a line Segment: Constructing a line can be achieved by one of the two methods.

• Construct a line and mark the length using a ruler.

• Construct a line and measure the length using a compass to mark an arc on the line.

Constructing a circle and semi-circle

To construct a circle of radius $3$ $3$ cm, a compass is used.?

Construction of a Circle : Measure the radius in a compass and mark a circle from the center point.

To construct a semi-circle of radius $3$ $3$ cm at point $A$ $A$ , a compass is used.

Constructing a Semicircle : Measure the radius using a compass and mark the semicircle from the center point.

Construction Line Segment by Copying

A line segment $¯ ¯¯¯¯ ¯ P Q$ $bar(PQ)$ is given. To copy the line segment $¯ ¯¯¯¯ ¯ P Q$ $bar(PQ)$ , a compass is used to measure the length of given line segment and mark that in another line.

Copying a line segment : Copy the length of the given line in a compass and construct an arc on a line.

Copying an angle

The following property helps to copy an angle using compass: "two triangles with identical sides have identical angles".

Given $/_ BAC$ . To copy this angle, make a triangle of random sides $/_\ APQ$ . Copy the length of line segment $bar(AQ)$ to mark point $L$ on the given line. Copy the lengths of line segments $bar(AP)$ and $bar(QP)$ to mark $M$ from points $X$ and $L$ respectively. Join the points $X$ and $M$ . The angle $/_BAC$ is reproduced in $/_LXM$ .

Copying a Given Angle : Mark a triangle in the given angle and reproduce the sides of a triangle which copies the angle.

summary

Construction of a line segment : The given length is measured using a ruler / scale and the line segment is marked. Construction of a circle of given radius : The given radius is measured in a compass and the circle is drawn. Construction of a semi circle of given radius : The given radius is measured in a compass and semi circle is drawn. Construction of a line by copying another line : The length of the given line is measured using a compass and the line segment is marked. Construction of an angle by copying another angle : A triangle is marked in the given angle and the sides of the triangle are reproduced to reproduce the angle.

Outline