Question

Ray BD is the line of symmetry for acute \[\angle ABC\]. The ray BD is also _____ of \[\angle ABC\].
A) Angle trisector
B) One arm
C) Angle bisector
D) None of these

Answer 1

Hint: Symmetry is an important aspect of geometry. We define the line of symmetry as the imaginary line where if we fold an image then both the halves of the figure match exactly. It means the line of symmetry divides the angle also. So, the line of symmetry is the angle bisector.

Complete step by step answer:
First, understand the concept of symmetry. A symmetry is a property possessed by a geometric figure which establishes a one to one correspondence with each angle and each vertex of the figure.
The symmetry is always observed along a line and that line is known as a line of symmetry.
We define the line of symmetry as the imaginary line where if we fold an image then both the halves of the figure match exactly.
Now, understand the meaning of the options,
Angle trisection is the division of an arbitrary angle into three equal angles. It was one of the three geometric problems of antiquity for which solutions using only compass and straightedge were sought.
An arm of an angle is either one of the two rays that form the angle.
An angle bisector divides the angle into two angles with equal measures. An angle only has one bisector. Each point of an angle bisector is equidistant from the sides of the angle.
Since the line of symmetry divides an angle into two equal angles i.e. it bisects the given angle.
So, the ray BD is also an angle bisector of \[\angle ABC\].

Hence, option (C) is the correct answer.

Note:
The line of symmetry is an imaginary line so you first need to visualize it. The line of symmetry need not be always parallel to any of the axis. It is a general line in the geometrical plane. The important point is it divides the given figure into two equal parts which exactly match.