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Constructions

Long Answer Type

11. Draw a line segment AB = 5 cm. From the point A draw a line segment AD = 6 cm making an angle of 60°. Draw perpendicular bisector of AD.

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12. Draw a line segment of 10 cm. Divide it into four equal parts. Write the measure of each part.

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13. Construct an equilateral triangle LMN, one of whose sides is 5 cm. Bisect ∠M of the triangle.

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14. Construct an angle ∠BAC = 90° on a line segment AB = 6 cm. Cut AC = 5 cm. Bisect AC at D. Measure AD and DC.

Steps of Construction

1. Draw a line segment AB = 6 cm.
2. Taking A as centre and some radius, draw an arc of a circle, which intersects AB, say at a point P.
3. Taking P as centre and with the same radius as before, draw an arc intersecting the previously drawn arc, say at a point Q.
4. Taking Q as centre and with the same radius as before, drawn an arc intersecting the arc drawn in step 1, say at R.
5. Next, taking Q and R as centres and with the radius more than $1 half$ QR, draw arcs to intersect each other, say at S.
6. Draw the ray AS.
7. From ray AS, cut off AC = 5 cm.

Then. ∠BAC = 90° is such that AB = 6 cm and AC = 5 cm.
8. Taking A and C as centres and radius more than $1 half$ AC. draw arcs on both sides of the line segment AC (to intersect each other).

Steps of Construction
1. Draw a line segment AB = 6 cm.2. Taking A

9. Let these arcs intersect each other at M and N. Join MN.
10. Let MN intersect AC at the point D.
Then, AD = DC
By measurement,
AD = DC = 2.5 cm

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Short Answer Type

15. Draw an acute angled triangle ABC. Construct perpendicular bisectors of AB and BC intersecting each other at O. Measure OA, OB and OC. Are they equal?

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16. Draw an angle of 40° with a protractor and then construct an angle 80° using ruler and compass.

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17. Construct an angle of 120° at the initial point of a given ray and justify the construction.

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18. Construct an angle of 150° at the initial point of a given ray and justify the construction.

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19. Using scale and compass, construct an equilateral triangle with one side as 4 cm and justify the construction.

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20. Draw a ∆ABC in which BC = 6 cm, AB = 5.2 cm and AC = 4.8 cm. Draw the perpendicular bisector of BC. Does it pass through A? (Use ruler and compass only).

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