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CBSE Class 10 Mathematics Worksheet

UNIT IV: Geometry - Constructions

1.

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?

2.

To divide a line segment AB in the ratio 4:5, first a ray AX is drawn so that is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is______.

A)

8

B)

9

C)

4

D)

3.

By geometrical construction, it is possible to divide a line segment in the ratio

A)

TRUE

B)

FALSE

4.

A pair of tangents can be constructed to a circle inclined at an angle of

A)

TRUE

B)

FALSE

5.

By geometrical construction, it is possible to divide a line segment in the ratio

A)

TRUE

B)

FALSE

6.

Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 3/4 of the corresponding sides of the first triangle?

7.

Divide a line segment AB of length 5 cm into 3:2 ratio

8.

To divide a line segment PQ in the ratio a : b (a, b are positive integers), draw a ray PX so that is an acute angle and then mark points on ray PX at equal distances such that the minimum number of these points is_____.

A)

a

B)

a - b

C)

9.

Construct a triangle similar to a given triangle PQR with PQ = 4cm, QR = 5 cm and PR = 6 cm with its sides equal to 4/5 of the corresponding sides of the triangle PQR?

10.

Divide a line segment PQ of length 7.2 cm into 5:6 ratio?

11.

Which theorem criterion we are using in giving the just the justification of the division of a line segment by usual method ?

A)

SSS criteria

B)

Basic proportionality theorem

C)

Pythagor

12.

A pair of tangents can be constructed to a circle inclined at an angle of ______.

A)

B)

C)

D)

13.

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?

14.

To divide a line segment AB in the ratio 4 : 5, draw a ray AX such that is an acute angle, then draw a ray BY parallel to AX and the points A1 , A2 , A3 , ... and B1 , B2, B3, ... are located at equal distances on ray AX and BY, respectively. Then the points joined are_______.

A)

A6 and B5

B)

A4 and B5

C)

A5 and B4

15.

To draw a pair of tangents to a circle which are at right angles to each other, it is required to draw tangents at end points of the two radii of the circle, which are inclined at an angle of_______.

A)

B)

C)

D)

16.

To draw a tangent at point B to the circumcircle of an isosceles right ΔABCright angled at B, we need to draw through B ______

A)

a line perpendicular to BC

B)

a line perpendicular to AB

C)

17.

Construct an isosceles triangle whose base 7 cm and altitude is 3.5 cm?

18.

To construct a triangle similar to a given with its sides 3/7 of the corresponding sides of , first draw a ray BX such that is an acute angle and X lies on the opposite side of A with respect to BC. Then locate points B1 , B2 , B3 , ... on BX at equal distances and next step is to join______.

A)

B10 to C

B)

B7 to C

C)

B3 to C

D)

19.

In division of a line segment AB, any ray AX making angle with AB is_____.

A)

right angle

B)

obtuse angle

C)

ac

20.

Two distinct tangents can be constructed from a point P to a circle of radius r situated at a distance.

A)

r from centre

B)

r/2 from centre

C)

More than r from centre

CBSE Class 10 Mathematics Worksheet

UNIT IV: Geometry - Constructions

Answers

1.

  1. With O as a centre and radius equal to 3 cm, a circle is drawn.

  2. The diameter of the circle is extended both sides and an arc is made to cut it at 7 cm.

  3. Perpendicular bisector of OP and OQ is drawn and X and Y be its mid-point.

  4. With O as a centre and OX be its radius, a circle is drawn which intersected the previous circle at M and N.

  5. Step 4 is repeated with O as centre and Oy as radius and it intersected the circle at R and T.

  6. PM and PN are joined also QR and QT are joined.

2.
Option B
3.
Option B
4.
Option A
5.
Option A

6.

  1. Construct triangle PQR using SSS criteria

  2. Locate 5  points Q1 , Q2 , Q3 , Q4  on QX so that QQ1 = Q1Q2 = Q2Q3 = Q3Q4

  3. Join Q3R and draw a line through Q3  parallel to Q5C to intersect QR at R′  

  4. Draw a line through R′ parallel to the line PR to intersect PQ at P′. Then, P′QR′ is the required triangle.

7.

  1. Draw a line segment AB = 5 cm

  2. Locate 5 points A1 , A2 , A3 , A4 and A5 on AX so that AA1 = A1 A2 = A2 A3 = A3 A4 = A4 A5

  3. Join BA5

  4. Through the point A3 , draw a line parallel to A5B (by making an angle equal to ) at A3 intersecting AB at the point C. Then, AC : CB = 3 : 2  

8.
Option C

9.

  1. Construct triangle PQR using SSS criteria

  2. Locate 5  points Q1 , Q2 , Q3 , Q4 , Q5 on QX so that QQ1 = Q1Q2 = Q2Q3 = Q3Q4 = Q4Q5

  3. Join Q5R and draw a line through Q4  parallel to Q5C to intersect QR at R′  

  4. Draw a line through R′ parallel to the line PR to intersect PQ at P′. Then, P′QR′ is the required triangle   

10.

  1. Draw a line segment AB = 7.2 cm

  2. Locate 5 points A1 , A2 , A3 , A4 , A5, A6, A7, A8, A9, A10 and A11 on AX so that AA1 = A1 A2 = A2 A3 = A3 A4 = A4 A5 =  A5A6=  A6 A7=  A7 A8=  A9 A10=  A10 A11

  3. Join BA11

  4. Through the point A5, draw a line parallel to A11B at A5 intersecting AB at the point C. Then, AC : CB = 5 : 6

11.
Option B
12.
Option B

13.

  1. Draw a circle of radius 6 cm with centre O.

  2. Draw PO = 10 cm and bisect it. Let M be the midpoint of PO where is P is outside the circle.

  3. Taking M as centre and MO as radius, draw a circle. Let it intersect the given circle at the points Q and R.

  4. Join PQ and PR. Then PQ and PR are the required two tangents.

14.
Option C
15.
Option D
16.
Option C

17.

  1. Draw a line AB = 7 cm

  2. From mid point D of AB draw a line CD = 3.5 cm perpendicular to AB.

  3. Join AC and BC and ABC is the required triangle.

18.
Option B
19.
Option C
20.
Option C

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