Perpendicular Bisector and Its Construction

Q.

Question 1

Draw $\overline{AB}$ of length 7.3 cm and find its axis of symmetry

Q.

Two lines perpendicular to a same line are parallel.

1. False

2. True

Q.

Question 2

Draw any line segment $\overline{PQ}$ Take any point R not on it. Through R, draw a perpendicular to $\overline{PQ}$ (Use ruler and set-square)

Q.

Question 75

Draw a line segment of length 7 cm. Draw its perpendicular bisector, using ruler and compass.

Q.

Draw any angle with vertex O. Take a point A on one of its arms and B on another such that OA = OB. Draw the perpendicular bisectors of $\overline{OA}$ and $\overline{OB}$. Let them meet at P. Is PA = PB?

Q.

Question 49

State whether the statements are true (T) or false (F).

Only one perpendicular bisector can be drawn to a given line segment.

Q.

Draw any line segment $\overline{AB}$. Mark any point $M$ on it. Through $M,$ draw a perpendicular to $\overline{AB}$. (Use ruler and compasses)

Q.

Question 88

Draw a line segment of length 6 cm. Construct its perpendicular bisector. Measure the two parts of the line segment.

Q.

Draw the perpendicular bisector of $\overline{XY}$ whose length is $10.3cm$

If $M$ is the mid-point of $\overline{XY}$, what can you say about the lengths $MX$ and $XY$?

Q.

Question 82

Draw a circle of radius 6 cm using ruler and compass. Draw one of its diameters. Draw the perpendicular bisector of this diameter. Does this perpendicular bisector contain another diameter of the circle?

Q. Question 4(iii)
Find the value of x in each of the following figures if l || m

Q.

Question 89

Draw a line segment of length 10 cm. Divide it into four equal parts. Measure each of these parts.

Q.

Question 56

In which of the following figures,

a) Perpendicular bisector is shown?

b) Bisector is shown?

c) only bisector is shown?

d) Only perpendicular is shown?

Q.

Draw a circle with radius $4cm$ and center P. Draw another circle of same radius and with center at Q such that it intersects the previous circle. Join PQ. Now join the points of intersection and name this line segment as AB. Mark the point of intersection of AB and PQ as O.

$\angle$AOP = __${}^{\circ }$

Q.

Question 76

Draw a line segment of length 6.5cm and divide it into four equal parts, using ruler and compass.

Q.

Construct a line segment AB of length 4.2 cm using a compass and a ruler. How many lines can be drawn from the point A? [2 MARKS]

Q.

Draw a line segment of length $5.3cm$and find its axis of symmetry.

Q.

Draw$AB$ of length$7.3cm$ and find its axis of symmetry.

Q.

Draw a line segment $\text{PQ = 6.8 cm}$. Draw a perpendicular to it from a point A outside PQ by using ruler and compass.

Q. Draw $\overline{AB}$ of length $7.3cm$ and find its axis of symmetry.

Q.

It is not possible to draw the perpendicular bisector of a line segment using a protractor with no markings on it.

1. True

2. False

Q.

Raghu walked along a path AB in 5 minutes. After some time he walked along the path PQ which happens to be twice as long as AB.
Construct the line PQ. [3 MARKS]

Q.

A perpendicular bisector of a given line is perpendicular to it and divides the given line into two parts of equal length.

1. is perpendicular to that line

2. divides that line in two equal parts

Q. Steps for the construction of a triangle ABC whose perimeter is 12.5 cm and whose base angles are ${60}^{\circ }$ and ${75}^{\circ }$ are given below. Choose the correct order.

1.Join AB and AC
2.Draw a line segment PQ of length 12.5cm
3.Construct rays PR such that $\angle QPR={60}^{\circ }$ and QS such that $\angle PQS={75}^{\circ }$
4.Draw the perpendicular bisector of AP and AQ and let these intersect PQ at B and C respectively.
5.Draw the bisectors PL and QM of $\angle QPR$ and $\angle PQS$ respectively. Let these intersect at A.

1. 2, 3, 1, 5, 4
2. 2, 3, 1, 5, 4
3. 2, 3, 5, 4, 1
4. 2, 3, 4, 1, 5

Q. Draw a circle of radius 5 cm and draw any two of its diameters. Find the figure obtained upon joining the ends of these diameters.​

Q. Draw a line segment PQ= 8 cm. Construct the perpendicular bisector of the line segment PQ. Let the perpendicular bisector drawn meets PQ at point R. Measure the length of PR and QR. Is PR=QR?

Q. X is the midpoint of the line segment AB. If AX is 9.3 cm, then the length of line segment AB is :

1. 4.65 cm
2. 18.6 cm
3. 9.3 cm
4. 18 cm

Q. Construct a perpendicular bisector of a given line segment.

Q. If a line segment $AB$ is bisected at point $P$ and through point $P$ another line segment $PQ$ which is perpendicular to $AB,$ is drawn then $QA=QB.$

1. True
2. False

Q. A line segment AC is bisected at B. Which of the following equals line segment AB ?

1. Line segment BC +AB
2. Line segment AB + AC
3. Line segment AC
4. Line segment BC