3. Draw the perpendicular bisector of XY whose length is 10.3 cm. (a) Take any point P on the bisector drawn. Examine whether PX = PY. (b) If M is the midpoint of XY, what can you say about the lengths MX and XY?

Follow the steps to draw the perpendicular bisector of a line XY.
a) PX= PY
b)MX=MY

**Q9. **Draw an angle of 40^{o}. Copy its supplementary angle.

The steps of constructions are:
(a) Draw an angle of 40 degrees with the help of protractor, naming ∠ AOB.
(b) Draw a line PQ.
(c) Take any point M on PQ.
(d) Place the compasses at O and draw an arc to cut the rays of ∠AOB at L and N.
(e) Use the same compasses setting to draw an arc O as the centre, cutting MQ at X.
(f) Set your compasses to length LN with the same radius.
(g) Place the...

**Q8. **Draw an angle of 70^{o}. Make a copy of it using only a straight edge and compasses.

The steps of constructions are:
(a) Draw an angle 70 degrees with a protractor, i.e., ∠POQ = 70 degrees
(b) Draw a ray AB.
(c) Place the compasses at O and draw an arc to cut the rays of ∠POQ at L and M.
(d) Use the same compasses, setting to draw an arc with A as the centre, cutting AB at X.
(e) Set your compasses setting to the length LM with the same radius.
(f) Place the compasses pointer...

**Q7. **Draw an angle of measure 135° and bisect it.

The steps of constructions are:
(a) Draw a line PQ and take a point O on it.
(b) Taking O as the centre and convenient radius, mark an arc, which intersects PQ at A and B.
(c) Taking A and B as centres and radius more than half of AB, draw two arcs intersecting each other at R.
(d) Join OR. Thus, ∠QOR = ∠POQ = 90 .
(e) Draw OD the bisector of ∠POR. Thus, ∠QOD is the required angle of 135.
(f)...

**Q6. **Draw an angle of measure 45° and bisect it.

The steps of constructions are:
1. Draw a ray OA
2. Taking O as the centre and convenient radius, mark an arc, which intersects OA at X.
3. Taking X as a centre and the same radius, cut the previous arc at Y. Taking Y as the centre and the same radius, draw another arc intersecting the same arc at Z.
4. Taking Y and Z as centres and the same radius, draw two arcs intersecting each other at S....

**Q5. **Construct with ruler and compasses, angles of following measures:

(f) 135^{o}

The steps of constructions are:
1. Draw a line PQ and take a point O on it.
2. Taking O as the centre and convenient radius, mark an arc, which intersects PQ at A and B.
3. Taking A and B as centres and radius more than half of AB, draw two arcs intersecting each other at R. Join OR. Thus, ∠QOR = ∠POR = 90°.
4. Draw OD the bisector of ∠POR. Thus, ∠QOD is required angle of 135°

**Q5. **Construct with ruler and compasses, angles of following measures:

(e) 45^{o}

The steps of constructions are:
1. Draw a ray OA
2. Taking O as the centre and convenient radius, mark an arc, which intersects OA at X.
3. Taking X as the centre and the same radius, cut the previous arc at Y. Taking Y as the centre and the same radius, draw another arc intersecting the same arc at Z.
4. Taking Y and Z as centres and the same radius, draw two arcs intersecting each other at...

**Q5. **Construct with ruler and compasses, angles of following measures:

(d) 120^{o}

The steps of constructions are:
1. Draw a ray OA
2. Taking O as the centre and convenient radius, mark an arc, which intersects OA at P.
3. Taking P as the centre and same radius, cut previous arc at Q. Taking Q as the centre and the same radius cut the arc at S. Join OS. Thus, ∠AOS is the required angle of 120°.

**Q5. **Construct with ruler and compasses, angles of following measures:

(c) 90^{o}

**Q5. **Construct with ruler and compasses, angles of following measures:

(b) 30^{o}

The steps of constructions are:
1. Draw a ray OA.
2. Taking O as the centre and convenient radius, mark an arc, which intersects OA at P.
3. Taking P as the centre and the same radius, cut the previous arc at Q. Join OQ. Thus, ∠BOA is the required angle of 60°.
4. Put the pointer on P and mark an arc.
5. Put the pointer on Q and with the same radius, cut the previous arc at C. Thus, ∠COA is...

**Q5. **Construct with ruler and compasses, angles of following measures:

(a) 60^{o}

The steps of constructions are:
1. Draw a ray OA
2. Taking O as the centre and convenient radius, mark an arc, which intersects OA at P.
3. Taking P as the centre and the same radius, cut the previous arc at Q. Join OQ. Thus,∠BOA is the required angle of 60°

**Q4. **Draw an angle of measure 153° and divide it into four equal parts.

The steps of constructions are:
(a) Draw a ray OA.
(b) At O, with the help of a protractor, construct ∠AOB = 153 degrees.
(c) Draw OC as the bisector of ∠AOB.
(d) Again, draw OD as bisector of ∠AOC.
(e) Again, draw OE as bisector of,∠BOC.
(f) Thus, OC, OD, and OE divide ∠AOB into four equal parts.

**Q3. **Draw a right angle and construct its bisector.

The steps of construction:
(a) Draw a line PQ and take a point O on it.
(b) Taking O as the centre and convenient radius, draw an arc that intersects PQ at A and B.
(c) Taking A and B as centres and radius more than half of AB, draw two arcs which intersect each other at C.
(d) Join OC. Thus, ∠COQ is the required right angle.
(e) Taking B and E as centre and radius more than half of BE, draw...

**Q2. **Draw an angle of measure 147° and construct its bisector.

The steps of constructions are:
1. Draw a line OA.
2. Using protractor and centre 'O draw an angle AOB =147°.
3. Now taking 'O' as the centre and any radius draws an arc that intersects 'OA' and 'OB' at p and q.
4. Now take p and q as centres and radius more than half of PQ, draw arcs.
5. Both the arcs intersect at 'R'
6. Join 'OR' and produce it.
7. 'OR' is the required bisector of...

**Q1. **Draw POQ of measure 75° and find its line of symmetry.

Here, we will draw using a protractor.
We follow these steps:
1. Draw a ray OA.
2. Place the centre of the protractor on point O, and coincide line OA and Protractor line
3. Mark point B on 75 degrees.
4. Join OB
Therefore
Now, we need to find its line of symmetry
that is, we need to find its bisector.
We follow these steps
1. Mark points C and D where the arc intersects OA and OB
2. Now,...

**Q9. **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 and . Let them meet at P. Is PA = PB ?

The steps of constructions are:
(i) Draw any angle with vertex O.
(ii) Take a point A on one of its arms and B on another such that
(iii) Draw perpendicular bisector of and .
(iv) Let them meet at P. Join PA and PB.
With the help of divider, we obtained that

**Q8. **Draw a circle of radius 4 cm. Draw any two of its chords. Construct the perpendicular bisectors of these chords. Where do they meet?

The steps of constructions are:
(i) Draw the circle with O and radius 4 cm.
(ii) Draw any two chords and in this circle.
(iii) Taking A and B as centres and radius more than half AB, draw two arcs which intersect each other at E and F.
(iv) Join EF. Thus EF is the perpendicular bisector of chord .
(v) Similarly draw GH the perpendicular bisector of chord .
These two perpendicular bisectors...

**Q7. **Repeat Question 6, if AB happens to be a diameter.

The steps of constructions are:
(i) Draw a circle with centre C and radius 3.4 cm.
(ii) Draw its diameter
(iii) Taking A and B as centres and radius more than half of it, draw two arcs which intersect each other at P and Q.
(iv) Join PQ. Then PQ is the perpendicular bisector of
We observe that this perpendicular bisector of passes through the centre C of the circle.

**Q6. **Draw a circle with centre C and radius 3.4 cm. Draw any chord . Construct the perpendicular bisector of and examine if it passes through C.

The steps of constructions are:
(i) Draw a circle with centre C and radius 3.4 cm.
(ii) Draw any chord .
(iii) Taking A and B as centres and radius more than half of , draw two arcs which cut each other at P and Q.
(iv) Join PQ. Then PQ is the perpendicular bisector of .
This perpendicular bisector of passes through the centre C of the circle.

**Q5. **With PQ of length 6.1 cm as diameter, draw a circle.

The steps of constructions are:
(i) Draw a line segment = 6.1 cm.
(ii) Draw the perpendicular bisector of PQ which cuts, it at O. Thus O is the mid-point of .
Taking O as the centre and OP or OQ as radius draw a circle where the diameter is the line segment .

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