NCERT Solutions 10th Maths Chapter 11 Constructions Exercise 11.1

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Exercise 11.1
1.Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts.
Solution:
Steps of Construction:
1. Draw a line segment AB = 7.6 cm.
2. Draw another line segment (or ray) AX at any convenient acute angle with AB.
3. Along AX, locate 13 (5 + 8) points A1, A2, A3, …… , A13 such that AA1 = A1A2 = ……… = A12A13
4. Join BA13.

2.Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are 2/3 of the corresponding sides of the first triangle.
Solution:
Steps of Construction:
1. Draw AC – 6 cm (ii) With A and Cas centers and radii 4 cm.
2. 5 cm respectively draw two ares intersecting each other at B. Join BA and BC.
3. Draw a ray AY making an acute angle with AC.
4. Locate three points and Ron AY, such that AP – POQR.
5. Join CR.
6. Through o. draw a line QC’ parallel to RC (by making an angle equal to ∠ARC) meeting the line segment AC at C’.

7. Similarly, through C, draw a line B’C parallel to CB Thus, ABC is the required triangle, which is similar to ∆ABC with scale factor 2 - 3 Justification:
By construction, we have: