Construction of Perpendicular Bisector and its Proof

Q.

Construct a triangle ABC in which BC is 5 cm, $\angle B$ is ${60}^{\circ }$ 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.

1. True

2. False

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

Q.

Construct a triangle ABC in which BC is 5 cm, $\angle B$ is ${60}^{\circ }$ and AB + AC = 10cm. Which type of triangle is this? [3MARKS]

Q.

A perpendicular bisector of a given line segment

1. is parallel to that line

2. is perpendicular to that line

3. divides that line in two equal parts

4. Both A and B

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

1. Any random point
2. Point of trisection
3. End point
4. Mid Point

Q. Construct the incircle of the triangle ABC with AB = 7 cm, $\angle$B = 50${}^{\circ }$ and BC = 6 cm. Then its inradius will measure

1. 1.5 cm
2. 1.8 cm
3. 2.1 cm
4. 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 triangle.

1. equilateral
2. obtuse
3. right-angled
4. 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.

1. True
2. False

Q.

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

1. True

2. False

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

Q.

The perpendicular bisector divides a line segment into __ parts.

1. 4
2. 0

3. 2

4. 3

Q.

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

1. AC = CB

2. AD = DB

3. OC = OD

4. 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:

1. is perpendicular to that line

2. divides that line in two equal parts

3. is parallel to that line

4. Both A and B

Q. Construct a triangle ABC in which BC is 5 cm, $\angle B$ is ${60}^{\circ }$ 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 triangle.

1. equilateral
2. obtuse
3. right-angled
4. scalene

Q. In the construction of a triangle ABC in which BC = 6 cm, $\angle B={45}^{\circ }$ and AB - AC = 2.5 cm, how many perpendicular bisectors are drawn?

1. 1
2. 2
3. 3
4. 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.

1. True
2. False

Q. In the construction of a triangle ABC in which BC = 6 cm, $\angle B={45}^{\circ }$ and AB - AC = 2.5 cm, how many perpendicular bisectors are drawn?

1. 1
2. 2
3. 3
4. 4

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

1. equilateral
2. obtuse
3. scalene
4. 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.

1. Both the statements are true
2. Only Statement 1 is true
3. Only Statement 2 is true
4. 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 $BC=8cm,\angle B={45}^{\circ }andAB-AC=3.5cm$.

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

1. equilateral
2. obtuse
3. right-angled
4. scalene

Q.

Construct a triangle ABC in which BC is 8 cm, $\angle$ B is ${70}^{\circ }$ 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, $\angle B={45}^{\circ }$ and AB - AC = 2.5 cm, how many perpendicular bisectors are drawn?

1. 1
2. 2
3. 3
4. 4

Q.

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

1. perpendicular bisector
2. angular bisector
3. median
4. altitude

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

1. AP = BP
2. AP = BQ
3. $\angle AOP$ = $\angle BOP$
4. 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 triangle.

1. obtuse
2. right-angled
3. scalene
4. equilateral