Geometry Construction solution of ncert exercise 11.1 part 1 Class Ten Mathematics

Geometry Construction

Exercise 11.1

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

Solution: Draw a line segment AB = 7.6 cm.

Draw a ray AX which makes an acute angle with AB.

Locate 13 points (5 + 8) A1, A2, A3, …….A13 on AX so that;

AA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6 = A6A7 = A7A8 = A8A9 = A9A10 = A10A11 = A11A12 = A12A13


geometry construction exercise solution

Join A13 to B.

Through the point A5, draw a line A5C || A13B; which intersects AB at point C.

We get; AC : CB = 5 : 8

AC = 2.92 cm and CB = 4.68 cm

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

Solution: Making the triangle.

geometry construction exercise solution

Dividing the base in 2 : 3 ratio:

Triangle AB’C’ is the required triangle.

Question 3: 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.

Solution: Making the triangle

geometry construction exercise solution

Dividing the base:

Triangle AB’C’ is the required triangle.

Question 4: Construct and isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 3/2 times the corresponding sides of the isosceles triangle.

Solution: Making the triangle:

geometry construction exercise solution

Triangle A’B’C’ is the required triangle.


Question 5: Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60o. Then construct a triangle whose sides are ¾ of the corresponding sides of the triangle ABC.

Solution: Making the triangle:

geometry construction exercise solution

Dividing the base:

Triangle A’C’B is the required triangle.

Question 6: Draw a triangle ABC with side BC = 7 cm, ∠B = 45o, ∠A = 105o. Then construct a triangle whose sides are 4/3 times the corresponding sides of triangle ABC.

Solution: Making the triangle:

geometry construction exercise solution

Dividing the Base:

Triangle A’BC’ is the required triangle.

Question 7: Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 m and 3 cm. Then construct another triangle whose sides are 5/3 times the corresponding sides of the given triangle.

Solution: Making the triangle:

Draw a line segment AB = 3 cm.

Make a right angle at point A and draw AC = 4 cm from this point.

Join points A and B to get the right triangle ABC.

geometry construction exercise solution

Dividing the base:

Triangle A’B’C’ is the required triangle.



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