Maths-

General

Easy

Question

# 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.

- Perpendicular Bisector Theorem:

- 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.

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.

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