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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 40o. 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 70o. 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)    135o

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)    45o

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)    120o

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)    90o

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:

                (b)    30o

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) 60o

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 \anglePOQ 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 \overline{OA} and \overline{OB}. 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 \overline{AB}. Construct the perpendicular bisector of \overline{AB} 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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