While constructing an equilateral triangle of a desired side, why using a compass is more efficient than a ruler?
Answer:
Method - 1: Using a ruler and a pencil.
To construct a triangle \(ABC\) using ruler and a pencil we follow the following procedure:
Step 1: Begin by drawing the base \(AB\) of the .
Step - 2: Locate the third using a ruler such that the sides \(AC\) and \(BC\) are of the desired lengths.
Method - 2: Using a compass, a ruler and a pencil.
To construct a triangle \(ABC\) using compass, ruler and a pencil we follow the following procedure:
Step - 1: Begin by drawing the \(AB\) of the required length.
Step - 2: Using a compass, construct a sufficiently long arc of radius equal to the from \(A\).
Step - 3: Now, construct another arc of radius equal to the from \(B\).
Step - 4: Mark the of the two arcs as \(C\). Now, join \(AC\) and \(BC\) to get the required triangle.
Interpretation:
Constructing a triangle using might require to determine the correct position of the . Alternately, constructing a triangle using enables determination of the , ensuring accuracy and efficiency.