NCERT Solutions for Class 10 Maths Exercise 11.1

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NCERT Solutions for Class 10 Maths Exercise 11.1 Class 10 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 10 Maths chapter wise NCERT solution for Maths Book for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

NCERT solutions for Maths Constructions Download as PDF

NCERT Solutions for Class 10 Maths Exercise 11.1

NCERT Solutions for Class 10 Maths Constructions

n each of the following, give the justification of the construction also:

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

Ans. Given: A line segment of length 7.6 cm.

To construct: To divide it in the ration 5: 8 and to measure the two parts.

Steps of construction:

(a) From any ray AX, making an acute angle with AB.

(b) Locate 13 (=5 + 8) points on AX such that.

(c) Join.

(d) Through the point, draw a line parallel to intersecting AB at the point C.

Then, AC: CB = 5: 8

On measurement, AC = 3.1 cm, CB = 4.5 cm

Justification:

[By construction]

[By Basic Proportionality Theorem]

But [By construction]

Therefore,

AC: CB = 5: 8


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

Ans. To construct: To construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are of the corresponding sides of the first triangle.

Steps of construction:

(a) Draw a triangle ABC of sides 4 cm, 5 cm and 6 cm.

(b) From any ray BX, making an acute angle with BC on the side opposite to the vertex A.

(c) Locate 3 points on BX such that.

(d) Join and draw a line through the point, draw a line parallel to intersecting BC at the point C’.

(e) Draw a line through C’ parallel to the line CA to intersect BA at A’.

Then, A’BC’ is the required triangle.

Justification:

[By construction]

[By Basic Proportionality Theorem]

But [By construction]

Therefore,

………(i)

CA C’A’ [By construction]

BC’A’ BCA [AA similarity]

[From eq. (i)]


NCERT Solutions for Class 10 Maths Exercise 11.1

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

Ans. To construct: To construct a triangle of sides 5 cm, 6 cm and 7 cm and then a triangle similar to it whose sides are of the corresponding sides of the first triangle.

Steps of construction:

(a) Draw a triangle ABC of sides 5 cm, 6 cm and 7 cm.

(b) From any ray BX, making an acute angle with BC on the side opposite to the vertex A.

(c) Locate 7 points on BX such that.

(d) Join and draw a line through the point, draw a line parallel to intersecting BC at the point C’.

(e) Draw a line through C’ parallel to the line CA to intersect BA at A’.

Then, A’BC’ is the required triangle.

Justification:

C’A’CA [By construction]

ABCA’BC’ [AA similarity]

[By Basic Proportionality Theorem]

[By construction]

[AA similarity]

But [By construction]

Therefore,


NCERT Solutions for Class 10 Maths Exercise 11.1

4. Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are times the corresponding sides of the isosceles triangle.

Ans. To construct: To construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then a triangle similar to it whose sides are of the corresponding sides of the first triangle.

Steps of construction:

(a) Draw BC = 8 cm

(b) Draw perpendicular bisector of BC. Let it meets BC at D.

(c) Mark a point A on the perpendicular bisector such that AD = 4 cm.

(d) Join AB and AC. Thus ABC is the required isosceles triangle.

(e) From any ray BX, making an acute angle with BC on the side opposite to the vertex A.

(f) Locate 3 points on BX such that.

(g) Join and draw a line through the point, draw a line parallel to intersecting BC at the point C’.

(h) Draw a line through C’ parallel to the line CA to intersect BA at A’.

Then, A’BC’ is the required triangle.

Justification:

C’A’CA [By construction]

ABCA’BC’ [AA similarity]

[By Basic Proportionality Theorem]

[By construction]

[AA similarity]

But [By construction]

Therefore,


NCERT Solutions for Class 10 Maths Exercise 11.1

5. Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ABC = Then construct a triangle whose sides are of the corresponding sides of triangle ABC.

Ans. To construct: To construct a triangle ABC with side BC = 6 cm, AB = 5 cm and ABC = and then a triangle similar to it whose sides are of the corresponding sides of the first triangle ABC.

Steps of construction:

(a) Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ABC = .

(b) From any ray BX, making an acute angle with BC on the side opposite to the vertex A.

(c) Locate 4 points on BX such that.

(d) Join and draw a line through the point, draw a line parallel to intersecting BC at the point C’.

(e) Draw a line through C’ parallel to the line CA to intersect BA at A’.

Then, A’BC’ is the required triangle.

Justification:

[By construction]

[By Basic Proportionality Theorem]

But [By construction]

Therefore, ………(i)

CA C’A’ [By construction]

BC’A’ BCA [AA similarity]

[From eq. (i)]


NCERT Solutions for Class 10 Maths Exercise 11.1

6. Draw a triangle ABC with side BC = 7 cm, B = A = Then construct a triangle whose sides are times the corresponding sides of ABC.

Ans. To construct: To construct a triangle ABC with side BC = 7 cm, B = and C = and then a triangle similar to it whose sides are of the corresponding sides of the first triangle ABC.

Steps of construction:

(a) Draw a triangle ABC with side BC = 7 cm, B = and C = .

(b) From any ray BX, making an acute angle with BC on the side opposite to the vertex A.

(c) Locate 4 points on BX such that.

(d) Join and draw a line through the point, draw a line parallel to intersecting BC at the point C’.

(e) Draw a line through C’ parallel to the line CA to intersect BA at A’.

Then, A’BC’ is the required triangle.

Justification:

[By construction]

[AA similarity]

[By Basic Proportionality Theorem]

But [By construction]

Therefore, ………(i)

CA C’A’ [By construction]

BC’A’ BCA [AA similarity]

[From eq. (i)]


NCERT Solutions for Class 10 Maths Exercise 11.1

7. 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 times the corresponding sides of the given triangle.

Ans. To construct: To construct a right triangle in which sides (other than hypotenuse) are of lengths 4 cm and 3 cm and then a triangle similar to it whose sides are of the corresponding sides of the first triangle ABC.

Steps of construction:

(a) Draw a right triangle in which sides (other than hypotenuse) are of lengths 4 cm and 3 cm.

(b) From any ray BX, making an acute angle with BC on the side opposite to the vertex A.

(c) Locate 5 points on BX such that.

(d) Join and draw a line through the point, draw a line parallel to intersecting BC at the point C’.

(e) Draw a line through C’ parallel to the line CA to intersect BA at A’.

Then, A’BC’ is the required triangle.

Justification:

[By construction]

[AA similarity]

[By Basic Proportionality Theorem]

But [By construction]

Therefore, ………(i)

CA C’A’ [By construction]

BC’A’ BCA [AA similarity]

[From eq. (i)]

NCERT Solutions for Class 10 Maths Exercise 11.1

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