Construction of a Perpendicular Bisector

Q.

A line segment when extended indefinitely in one direction is called .................

1. Ray.

2. Line.

3. Line segment.

4. None of these.

Q.

In the adjoining figure, $BM\perp AC$ and $DN\perp AC$. If $BM=DN$, prove that $AC$ bisects $BD$.

Q.

Draw a line segment of length 8.6 cm. Bisect it and measure the length of each part.

Q.

Draw the perpendicular bisector of a line segment of length 5 cm.

Q. AB is a line segment and line l is its perpendicular bisector. Show that every point on line l is equidistant from A and B.

Q. Construct $∆$XYZ such that XY = 6.7 cm , YZ = 5.8 cm, XZ = 6.9 cm and constructs its incircle.

Q.

Draw a line segment AB of length 5.8 cm. Draw the perpendicular bisector of this line segment.

Q. We draw a line segment $PQ$ of length $5cm$. We take an external point $A$ of line segment. Let us draw paralel line through the point A to line segment PQ. [Let us draw three alternative process]

Q.

Draw a line segment AB=5.6 cm and draw its perpwndicular bisector. Measure the length of each part.

Q. Construct a perpendicular bisector to the line segment AB=12cm.

Q. For constructing a perpendicular bisector, the arc radius is more than ____ of the line segment.

1. half
2. one third
3. one fourth
4. one fifth

Q.

In the construction of the perpendicular bisector of a given line segment, as shown in the figure below

$\Delta PMA\cong \Delta PMB$ by which congruence criterion?

1. AAS

2. RHS

3. SSS

4. SAS

Q.

Draw a circle with centre at point O. Draw its two chords AB and CD such that AB is not parallel to CD. Draw the perpendicular bisectors of AB and CD. At what point do they intersect ?

Q.

Taking the line segment of length $4.5cm$ as a diameter. Draw a circle.

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.

Bisector AD of $\angle BAC$ of $\Delta ABC$ passes through the centre O of the circumcircle of $\Delta ABC$. Prove that AB = AC. [2 MARKS]

Q.

Draw any line $m$ and mark any point $A$ outside it. Through this point, construct a line perpendicular to $m$ by using a ruler and set square.

Q. How many arcs required to draw the perpendicular bisector in Triangle Construction 1?

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

Q.

Draw the perpendicular bisector of a line segment of length 6.4 cm. Also, measure the length of each bisected part.

Q.

To construct a parallelogram___

1. two adjacent sides and the angle between them

2. one angle and a side

3. one diagonal

4. two adjacent angles and the side between them

Q.

Is the length of perpendicular bisector of a line segment, finite or infinite?

__

Q.

Draw a line $l$ and a point $X$ on it. Through $X$ , draw a line segment $\overline{XY}$ perpendicular to $l$. Now draw a perpendicular to $\overline{XY}$ at $Y$. (Use a ruler and compass).

Q.

If AE = BE, then CD is the perpendicular bisector of line segment AB.

1. True

2. False

Q. Construct $∆$LMN in base MN = 7 cm, $\angle$LMN = 40$°$ and LM $-$ LN = 3cm.

Q. Draw a circle with centre at point O. Draw its two chords AB and CD such that AB is not parallel to CD. Draw the perpendicular bisectors of AB and CD. At what point do they intersect?

Q. Draw a line segment AB of length 5.8 cm. Draw the perpendicular bisector of this line segment.

Q.

Construct a triangle $ABC$ in which $BC$ equal to $7cm$, Angle $B$ equal to $75$ degree and $AB+AC$ equal to $13cm$.

Q. Draw a circle with centre at point O. Draw its two chords AB and CD such that AB is not parallel to CD. Draw the perpendicular bisectors of AB and CD. At what point do they intersect ?

Q.

The perpendicular bisector is a line segment.

1. True

2. False

Q.

If ST = RT, then PQ is the perpendicular bisector of line segment SR.

1. True

2. False