State and prove the Perpendicular Bisector Theorem.

The correct answer is: Hence proved.

Answer:

• To prove: 
• Perpendicular Bisector Theorem:

• Proof: 
• Statement:
• According to perpendicular bisector theorem, in the triangle, any point on perpendicular bisector is at equal distance from both end points of the line segment on which it is drawn.

• Step 1:

Let consider given figure,

Let arbitrary point C on perpendicular bisector.
In which,
CD is perpendicular bisector on AB.
Hence,
AD = DB
CD = CD (common)

So, according to SAS rule

Hence,
CA = CB
So, any point on perpendicular bisector is at equal distance from end points of line segment.
Hence proved.