Geometry is an ancient science and an important branch of mathematics. Everyday we come across many shapes in daily life, we call them geometrical shapes. The idea of construction came from these shapes. Consider a triangle, a rectangle, a square or any other shape. Every shape begins with a point and then extends to be a line or a line segment or a curve. Number and arrangement of these line segments decides the type of figure. To construct any geometrical figure we need to have an idea to construct a line segment. Let’s learn how to construct a replica of a given line segment.
Construction In Geometry
In geometry, construction means drawing lines, shapes or angles accurately using pencils, rulers and compasses. This is the pure geometric construction i.e. no measurements, no numbers. So let’s learn pure geometric constructions of a line segments step by step.
A point is a small dot which is the starting point of a line segment. By definition a line segment is a part of line which connects two points within a line. Different numbers of line segments gives us different figures and such figures may be either open figure or closed figures. A line segment is denoted by its two endpoints. In figure, m is a line and AB is the line segment on the line m.
Construction Of A Copy Of Line Segments
We can construct a line segment of a given length either by using a ruler or a combination of ruler and compass. Construction of a copy of a given line segment can also be achieved easily by using either of the above methods. However, construction of line segments is not that accurate when we use a ruler only. Hence, a ruler-compass combination is always the better approach to construct a copy of line segments.
Let’s construct a copy of a line segment () using ruler and compass together.
Step 1: Let be a line segment of unknown length.
Step 2: Fix the compass’ pointer on the point X and pencil pointer on Y gives you the length of.
Step 3: Now draw a straight line using a ruler, let’s say line m().
Step 4: Mark a point A onand fix the compass pointer (step 2)on A without changing the settings.
Step 5: Fixing compass on A draw an arc on, name the point at which pencil pointer cuts as B.
Now is a copy of i.e. length of AB will same as that of XY (if you didn’t change the compass settings).
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