Answer:
The two triangles are congruent, so any point on CD will be equidistant from endpoints of AB.
Step-by-step explanation:
Let the consider the figure as per the attached image:
AB be a line whose perpendicular bisector line is CD.
CD divides the line AB in two equal line segments making an angle of on both the sides as shown in the attached figure.
Let a point on CD be E.
Here, two triangles are formed:
Side ED is common between the two triangles.
Also, Side ED is perpendicular bisector:
And Sides AD = DB
According to SAS congruence (i.e. Two sides are equal and angle between them is equal):
And as per the <em>properties of congruent triangles, all the sides are equal.</em>
EA and EB is the distance of point E on line CD from the endpoints of line AB.
Hence proved that Any point on CD is equidistant from the endpoints of AB .
