# Construction of Perpendicular Bisector and its Proof

## Trending Questions

**Q.**

Construct a triangle ABC in which BC is 5 cm, ∠B is 60∘ and AB - AC=0 cm. What type of triangle is this? [4 MARKS]

**Q.**There is a line segment AB. Choose the correct statements about its perpendicular bisector.

True

False

- Every point in the perpendicular bisector is equidistant from point A and B.
- None of these.

**Q.**

Construct a triangle ABC in which BC is 5 cm, ∠B is 60∘ and AB + AC = 10cm. Which type of triangle is this? [3MARKS]

**Q.**

A perpendicular bisector of a given line segment

is parallel to that line

is perpendicular to that line

divides that line in two equal parts

Both A and B

**Q.**At what point does the perpendicular bisector of a line segment intersect the line segment?

- Any random point
- Point of trisection
- End point
- Mid Point

**Q.**Construct the incircle of the triangle ABC with AB = 7 cm, ∠B = 50∘ and BC = 6 cm. Then its inradius will measure

- 1.5 cm
- 1.8 cm
- 2.1 cm
- 2.3 cm

**Q.**

In the below figure if AP=BP, AQ=BQ, then AM=BM?

**Q.**

In the figure, PM is the perpendicular bisector of the segment AB. If C is some point on PM, then △ABC is

- equilateral
- obtuse
- right-angled
- scalene

**Q.**If a line is drawn through the mid point of one side of a triangle and parallel to the other side, it trisects the third side.

- True
- False

**Q.**

Which of the following statements is /are true regarding a perpendicular bisector?

True

False

- It passes through the given segment's midpoint.
- None of the above

**Q.**

The perpendicular bisector divides a line segment into

- 4
- 0
2

3

**Q.**

Which of the following relations does not have to be true in the construction of a perpendicular bisector?

AC = CB

AD = DB

OC = OD

AO = OB

**Q.**

What is the number of sections a perpendicular bisector divides a line segment into?

**Q.**

A perpendicular bisector of a given line:

is perpendicular to that line

divides that line in two equal parts

is parallel to that line

Both A and B

**Q.**Construct a triangle ABC in which BC is 5 cm, ∠B is 60∘ and AB - AC=0 cm. What type of triangle is this?

**Q.**

In the figure, PM is the perpendicular bisector of the segment AB. If C is some point on PM, then △ABC is

- equilateral
- obtuse
- right-angled
- scalene

**Q.**In the construction of a triangle ABC in which BC = 6 cm, ∠B=45∘ and AB - AC = 2.5 cm, how many perpendicular bisectors are drawn?

- 1
- 2
- 3
- 4

**Q.**If a line is drawn through the mid point of one side of a triangle and parallel to the other side, it trisects the third side.

- True
- False

**Q.**In the construction of a triangle ABC in which BC = 6 cm, ∠B=45∘ and AB - AC = 2.5 cm, how many perpendicular bisectors are drawn?

- 1
- 2
- 3
- 4

**Q.**

In the figure, PM is the perpendicular bisector of the segment AB. If C is some point on PM, then △ABC is

- equilateral
- obtuse
- scalene
- right-angled

**Q.**

AB is a line segment. With A and B as centres and any radius greater than half of AB, draw arcs on either side of AB so that they meet at X and Y as shown. Join XY

There are the two statements:

Statement 1: AB is the perpendicular bisector of XY

Statement 2: XY is the perpendicular bisector of AB

Choose the correct option from below.

- Both the statements are true
- Only Statement 1 is true
- Only Statement 2 is true
- None of the above

**Q.**

What is the number of sections a perpendicular bisector divides a line segment into?

**Q.**Find the sum of the number of angle bisector(s) and perpendicular bisector(s) drawn to construct a triangle ABC in which BC=8 cm, ∠B=45∘ and AB−AC=3.5 cm.

**Q.**

In the figure, PM is the perpendicular bisector of the segment AB. If C is some point on PM, then △ABC is

- equilateral
- obtuse
- right-angled
- scalene

**Q.**

Construct a triangle ABC in which BC is 8 cm, ∠ B is 70∘ and AB - AC = 7. [4 MARKS]

**Q.**

what is the diffrence between bisectors and perpendicular bisectors??

**Q.**In the construction of a triangle ABC in which BC = 6 cm, ∠B=45∘ and AB - AC = 2.5 cm, how many perpendicular bisectors are drawn?

- 1
- 2
- 3
- 4

**Q.**

Each point on a/an _________ is such that it forms an isosceles triangle with the end points of the given line segment.

- perpendicular bisector
- angular bisector
- median
- altitude

**Q.**PQ is the perpendicular bisector of AB. Then which of the following are correct?

- AP = BP
- AP = BQ
- ∠AOP = ∠BOP
- OB = OP

**Q.**

In the figure, PM is the perpendicular bisector of the segment AB. If C is some point on PM, then △ABC is

- obtuse
- right-angled
- scalene
- equilateral