MATHEMATICS WORKSHEET

QUESTIONS:1 mark -10 questions :- 10 x 1 = 102 mark -6 questions :- 6 x 2 = 124 mark -7 questions :- 7 x 4 = 28

TOTAL = 50 marks

( 10 x 1 = 10 m)1.___ factor means the ratio of the sides of the triangle

to be constructed with the corresponding sides of a given triangle.

2.A plane closed figure bounded by 3 straight lines.3.Only __ tangent (s) can be drawn from the point on

the circle.4.Name the type of the triangle in the figure (1)? 5.In figure(2) AB’C’ is similar to ABC , whose sides

are __ of the corresponding sides of ABC.

6.Number of points common to a circle & one of its tangents.

7.A curve made by moving one point at a fixed distance from another.

8.Measure <BCD in figure(3)?9.From figure(4) identify at what ratio is line segment AB divided?10. 2 circles are drawn with same centre . The 2 circles are known as:

( 6 x 2 = 12 m )11. Draw a circle of radius 6 cm. From a point 10 cm

away from its centre, construct the pair of tangents to the circle and measure their lengths.

12. Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding sides of the first triangle.

13. Construct a triangle of sides 4 cm, 5cm and 6cm and then a triangle similar to it whose sides are 2/3 of the corresponding sides of the first triangle.

14. Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts.

15. Construct a tangent to circle from a point P outside the circle using its centre O.

16. Construct a circum circle of a triangle ABC where a = BC, b = CA and c = AB.

( 7 x 4 = 28 m )

17. Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding sides of the first triangle. Give the steps of the construction.

18. Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle.

19. Construct a   to a equilateral  with side 5cm such that each its sides is 6/7th of the corresponding side of  Also draw the circum circle of .

20. Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

21. Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle. Write the steps of constructions.

22. Draw a triangle ABC with side BC = 7 cm, <B = 45°, <A = 105°. Then, construct a triangle whose sides are 4/3 times the corresponding side of <ABC. Write the steps of construction.

23. Let ABC be a right triangle in which AB = 6 cm, BC = 8 cm and <B = 90°. BD is the perpendicular from B on AC. The circle through B, C, and D is drawn. Construct the tangents from A to this circle.

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1. Scale2. Triangle3. One4. Right Triangle5. 2/36. One7. Arc8. 1109. 5:810. Concentric Circles

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17. Step 1 Draw a line segment AB of 5 cm. Taking A and B as centre, draw arcs of 6

cm and 5cm radius respectively. Let these arcs intersect each other at point C. <ABC is the required triangle having length of sides as 5 cm, 6 cm, and 7 cm respectively.

Step 2 Draw a ray AX making acute angle with line AB on the opposite side of

vertex C.Step 3 Locate 7 points, A1, A2, A3, A4 A5, A6, A7 (as 7 is greater between 5and

7), on line AX such that AA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6 = A6A7.

Step 4 Join BA5 and draw a line through A7 parallel to BA5 to intersect extended line segment AB at point B'.Step 5 Draw a line through B' parallel to BC intersecting the extended line segment AC at C'. <AB'C' is the required triangle.

18:Step 1Draw a line segment AB = 4 cm. Draw a ray SA making 90° with it.Step 2Draw an arc of 3 cm radius while taking A as its centre to intersect SA at C. Join BC. ABC is the required triangle.Step 3Draw a ray AX making an acute angle with AB, opposite to vertex C.Step 4Locate 5 points (as 5 is greater in 5 and 3), A1, A2, A3, A4, A5, on line segment AX , such that AA1 = A1A2 = A2A3 = A3A4 = A4A5.Step 5Join A3B. Draw a line through A5 parallel to A3B intersecting extended line segment AB at B'.Step 6Through B', draw a line parallel to BC intersecting extended line segment AC at C'.AB'C' is the required triangle.

19: A ray QX is drawn making any angle with QR and opposite to P. Starting from Q, seven equal line segments QQ1, Q1R2, Q2Q3, Q3Q4, Q4Q5, Q5Q6,

Q6Q7 are cut of from QX. RQ7 is joined and a line CQ6 is drawn parallel to RQ4 to intersect QR at C. Line CA is drawn parallel to PR.

ABC is the required triangle.

20:Step 1Taking any point O on the given plane as centre, draw a circle of 3 cm radius.

Step 2Take one of its diameters, PQ, and extend it on both sides. Locate two points on this diameter such that OR = OS = 7 cm

Step 3Bisect OR and OS. Let T and U be the mid-points of OR and OS respectively.

Step 4Taking T and U as its centre and with TO and UO as radius, draw two circles. These two circles will intersect the circle at point V, W, X, Y respectively. Join RV, RW, SX, and SY. These are the required tangents.

21:Step 1Draw a line segment AB of 8 cm. Taking A and B as centre, draw two circles of 4 cmand 3 cm radius.Step 2Bisect the line segment AB. Let the mid-point of AB be C. Taking C as centre, draw a circle ofAC radius which will intersect the circles at points P, Q, R, and S. Join BP, BQ, AS,and AR. These are the required tangents

22:

Step 1Draw a <ABC with side BC = 7 cm, ∠B = 45°, ∠C = 30°.Step 2Draw a ray BX making an acute angle with BC on the opposite side of vertex A.Step 3Locate 4 points (as 4 is greater in 4 and 3), B1, B2, B3, B4, on BX.Step 4Join B3C. Draw a line through B4 parallel to B3C intersecting extended BC at C'.Step 5Through C', draw a line parallel to AC intersecting extended line segment at C'.<A'BC' is the required triangle.

23:Step 1Join AE and bisect it. Let F be the mid-point of AE.

Step 2Taking F as centre and FE as its radius, draw a circle which will intersect the circle at point B and G. Join AG.AB and AG are the required tangents.

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