Perpendicular Bisector

Q.

Draw the perpendicular bisector of a line segment of length 8 cm.
[2 MARKS]

Q.

With $\overline{PQ}$ of length 6.1 cm as diameter, draw a circle.

Q. The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment , then it is:

1. Equidistant from the segment's endpoints
2. Equidistant from the the segment's midpoint
3. Perpendicular to the segment
4. Perpendicular to the segment's endpoints

Q.

Question 2
Draw a line l. Draw a perpendicular to l at any point on l. On this perpendicular choose a point X, 4 cm away from l. Through X, draw a line m parallel to l.

Q.

A ___ bisector is a line that divides the line segment into two equal halves and forms a right angle with the line segment

Q.

The perpendicular bisector of line segement AB meets AB at O. If AO = 6.5 cm, then AB = _____ cm.

1. 6.5 cm
2. 10 cm
3. 12 cm
4. 13 cm

Q. Question 7
Construct a rectangle whose adjacent sides are of lengths 5cm and 3.5cm.

Q.

On a line segment with length 7 cm, draw an arc at one end with radius 3 cm and another arc at the other end with radius 4 cm. The two arcs drawn will intersect at a point.

1. True

2. False

Q. Which one of the properties described below does not apply to the perpendicular bisector of a segment?

1. It is perpendicular to the original segment
2. It must be longer than the original segment
3. Every point on the perpendicular bisector is at the same distance from both endpoints of the segment.
4. It divides the original segment into two equal parts

Q. Draw a line segment of length 12.8 cm. Using compasses, divide it into four equal parts. Verify by actual measurement

Q.

Question 3 (a)

Draw the perpendicular bisector of $\overline{XY}$ whose length is 10.3 cm
Take any point P on the bisector drawn. Examine whether PX = PY.

Q. Question 9
In the given figure, the value of x is

(a) ${110}^{\circ }$
(b) ${46}^{\circ }$
(c) ${64}^{\circ }$
(d) ${150}^{\circ }$

Q. Fill in the blank :
A perpendicular bisector XY is constructed of line segment AB of length 2.4 cm. It meets line AB at O. Then OA = _____.

Q. In an right angled triangle, point of concurrence of perpendicular bisectors of its sides lies

1. On a side of the triangle
2. Inside the triangle
3. Outside the triangle
4. On a vertex of the triangle

Q.

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 in X and Y as shown. Join XY

These 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. Only Statement 1 is true

2. Both the statements are true

3. None of the statements are true

4. Only Statement 2 is true

Q.

Draw a line l. Then draw a perpendicular on l at any point. On this perpendicular, choose a point X, 5.5 cm away from l. Through X, draw a line m parallel to l. [3 MARKS]

Q.

The value of $x$ in the given figure is

1. ${40}^{\circ }$

2. ${85}^{\circ }$

3. ${120}^{\circ }$

4. ${12}^{\circ }$

Q. (a) Draw a line l. Draw a perpendicular on l at any point. On this perpendicular, choose a point X, 4 cm away from l. Through X, draw a line m parallel to l.

(b) Line l and m are parallel to each other. A transversal intersects them at points A and B.

i) An arc of suitable measure is taken from B cutting ‘l’ at D and transversal at M (as shown in the figure).

ii) Now, with the same radius and A as the centre an arc FG is drawn (as shown in the figure).

What is the relation between the length of arc DM and arc FG?
[4 MARKS]

Q.

There are many ways to do the construction of parallel lines and my Sir has told me different ways to solve different questions. How will I get to know that which method I will have to use for which question in the exam ?

Q. If MN, the perpendicular bisector of line segment AB meets it at O. Then AO = , when AB= 14cm.

1. 7cm
2. 28cm
3. 5cm

Q. Draw segment $PQ$ of length $7$ cm and bisect it.

Q.

Construct $\overline{PQ}$ of length $8.2$ cm. From this cut off $\overline{PR}$ of length $5.4$ cm. Measure $RQ$.

Q.

Infinitely many perpendicular bisectors can be drawn to a given line segment.

1. True
2. False

Q. Draw a line segment of 8cm length and construct a perpendicular bisector to line segment using scale and compass.

Q. To construct perpendicular bisector to a line segment AB =10 cm, we have to draw an arc of radius

1. $>5$
2. $<5$
3. $=5$

Q. If MN, the perpendicular bisector of line segment AB meets it at O. Then what is the length of AO when AB = 14cm.

1. 5 cm
2. 14 cm
3. 7 cm
4. 10 cm

Q. Find the value of $x$, if AB is the line segment and PQ is its perpendicular bisector.

1. ${90}^{\circ }$
2. 3.5 cm
3. 3 cm

Q. If the perpendicular bisector of line segment MN intersects it at point K, 10.2 cm from N, the length of MN is:

1. 20.4 cm
2. 5.1 cm
3. 10.2 cm
4. 10 cm

Q. Find the value of 'x', if AB is the line segment and PQ is its perpendicular bisector.

Q.

A perpendicular bisector of a line divides it into ___ equal parts.