# Important Questions for Chapter 11 - Constructions

Important questions based on NCERT syllabus for Chapter 11 - Constructions:

Question 1: Construct a 60∘ angle using a line segment of length of length 10 cm.
Solution:
Steps :

1. Draw a line segment AB of length 10 cm.
2. With A as centre draw an arc of any radius. Let this arc intersect AB at P.
3. With the same radius as before draw an arc with P as centre. Let this arc cut the previously drawn arc at Q.
4. Angle QAP is the required the 60∘ angle.
5. QA makes angle of 60∘ with line segment AB whose length is 10 cm.

Question 2: Construct 75∘ and verify by measuring it by a protractor.
Solution:
Steps :

1. Take the given ray PQ . Draw an arc of some radius taking point P as its centre, which intersects PQ at R.
2. Taking R as centre and with the same radius as before , draw an arc intersecting the previously drawn arc at S.
3. Taking S as centre and with the same radius as before, draw an arc intersecting the arc at T.
4. Taking S and T as centre, draw an arc of same radius to intersect each other at U.
5. Join PU. Let it intersect the arc at V. Taking S and V as centre, draw arcs with radius more than 12SV.
6. Let those intersect each other at W. Join PW which is the required ray making 75∘ with given ray PQ.

The angle so formed can be measured with the help of a protractor. It comes to be 75∘

Question 3: Construct a triangle ABC in which BC is 3 cm, ∠ B is 60∘ and AC - AB = 1 cm.
Solution:
Steps :

1. Draw a line segment BC = 3cm. Draw ray BX which makes an ∠60∘ with BC.
2. Cut off line segment BD of length AC - AB = 1 cm on BX on the opposite side of BC. Join CD.
3. Draw the perpendicular bisector of CD. Let the perpendicular bisector intersect ray BX at A.
4. Triangle ABC is the required triangle.