Question Video: Identifying Whether a Line Is a Line of Symmetry | Nagwa Question Video: Identifying Whether a Line Is a Line of Symmetry | Nagwa

# Question Video: Identifying Whether a Line Is a Line of Symmetry Mathematics • First Year of Preparatory School

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True or False: In the following figure, line πΆπ· is a line of symmetry of line segment π΄π΅.

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### Video Transcript

True or False: In the following figure, line πΆπ· is a line of symmetry of line segment π΄π΅.

Letβs begin by considering the figure and the line segment π΄π΅. We can observe in the figure that there are two pairs of arcs above and below the line segment. These arcs have been created by using a compass, which is a tool that we use when we are creating geometrical constructions. For example, in this construction, we began with the line segment π΄π΅. The compass was placed either on point π΄ or π΅ first; it doesnβt matter which. Here, we have placed it on point π΅. And arcs were drawn above and below the line segment like this. Then the compass point was placed on the other endpoint of the line segment. And a pair of arcs were drawn above and below the line segment again. The points of intersection of the arcs above and below were then joined with a line.

By doing so, we have created the perpendicular bisector of the line segment π΄π΅. This is also demonstrated in the original diagram. We can observe that there are two congruent line segments such that π΄π΅ has been bisected. And because of these important arcs, we know that this is a perpendicular bisector and therefore the line segments π΄π΅ and πΆπ· must be perpendicular.

We can now consider the problem, is the line πΆπ· a line of symmetry of line segment π΄π΅? And of course, it must be, because we know that we have these congruent line segments as π΄π΅ is bisected. If we reflected the left side onto the right side across the line πΆπ· or vice versa, then the two sections would fit exactly on top of one another.

So, the answer to the problem is true. Line πΆπ· is a line of symmetry of line segment π΄π΅.

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