Chapter 11 : Geometrical Construction

Construction 6. Construct a triangle ABC in which BC = 6cm, and the attitude through A is 4.5cm. Measure the length of median through A. Write the steps of construction.

Procedure:-

1. BC = 6cm is drawn and is made downwards with BC of any length.
2. is drawn
3. Perpendicular bisector RQ of BC is drawn which cut BC at M. and intersect BE at O.
4. Taking O as centre and OB as radius, a circle is drawn.
5. ML = 4.5cm is cut from RQ.
6. A line XY, parallel to BC is drawn through L to intersect the circle at A and A'.
   AB, AC, A’B and A’C are joined.
   ABC and A’BC are the required triangle
   Medium AM = A'M = 5.5cm (app.)

Construction 7. Construct a triangle ABC in which BC = 5cm, and median AD through A is of length 3.5cm. Also, determine the length of the altitude drawn from A on the side BC (Write the steps of construction also).

Procedure:-

1. BC = 5cm is drawn and is constructed downwards.
2. BX is drawn perpendicular to BY.
3. Q is drawn perpendicular bisector if BC intersecting BX at O and cutting BC at E.
4. Taking O as a centre and OB as radius, a circle is drawn.
5. Taking E as centre and radius equal to 3.5cm, arc is drawn to cut the circle at A.
6. AC and AB are joined
7. AD is drawn perpendicular to BC from A to cut BC at D.
8. By measuring we find that AD = 3cm.

Construction 8. Construction a to a equilateral with side 5cm such that each its sides is 6/7th of the corresponding side of Also draw the circumcircle of .

Procedure:-

1. A ray QX is drawn making any angle with QR and opposite to P.
2. Starting from Q, seven equal line segments QQ₁, Q₁R₂, Q₂Q₃, Q₃Q₄, Q₄Q₅, Q₅Q₆, Q₆Q₇ are cut of from QX.
3. RQ₇ is joined and a line CQ₆ is drawn parallel to RQ₄ to intersect QR at C.
4. Line CA is drawn parallel to PR.
   ABC is the required triangle.

Exercise - 23

Q. 1.Construct a triangle ABC in which BC = 5cm, and the altitude drawn from A on BC is of length 3,5cm.

Q. 2.Construct a triangle ABC in which BC = 7cm, and attitude through A is 3.7cm. How many such triangles are possible.

Q. 3.Construct a triangle ABC in which BC = 4cm, and altitude through A is 3cm. Also write the steps of construction.

Q. 4.Construction a triangle ABC with AB = 4.4cm, and the median through C is of length 3.2cm. Also, find the length of the altitude drawn from the vertex C on AB.

Q. 5.Construct a triangle ABC in which BC = 6cm, and the median through A is 5,5cm. Find the length of altitude drawn on BC from A. Write the steps of construction.

Q. 6.Construct a triangle ABC in which BC = 6cm, and median AD = 4.5cm.

Q. 7.Construct a triangle ABC in which BC = 6cm, and the altitude through A is 4.5cm. Measure the length of median through A.

Q. 8.Construct a triangle ABC in which BC = 6.4cm, and median AD = 5cm. How many such triangles are possible?

Q. 9.Construct a triangle ABC in which BC = 6cm, and the median from A on BC = 5cm. How many such triangles are possible?

Q. 10.Construct a triangle ABC similar to a give triangle PQR with QR = 6cm, PQ = PR = 5cm. Such that each of its side is 6/7th of the corresponding sides of the triangle PQR. Also draw the circumcircle of triangle ABC.

Q. 11.Construct a triangle ABC in which AB = 5cm, and altitude CD = 3cm. Construct a triangle AQR similar to triangle ABC such that each side of triangle AQR is 1.5 times that of the corresponding side of triangle ABC.

Q. 12.Construct a triangle ABC with BC = 6cm, and median AD through A is 5cm long. Construct a triangle A’BC’ similar to triangle ABC with BC = 8cm.

Q. 13.Construct a triangle ABC in which BC = 6.5cm, m and median through A is 4.5cm construct a triangle A’BC’ similar to triangle ABC with BC = 8cm.

Q. 14.Construct a quadrilateral ABCD in which AB = 3cm, AD2.7cm, DB = 3.6cm, and BC = 4.2cm. Construct a quadrilateral A’BC’ D’ similar to quadrilateral ABCD is which diagonal D’B is of length 4.5cm

Q. 15.Draw any quadrilateral ABCD. Construct another quadrilateral AB’C’D’ similar to the each side equal to 4/5th of the corresponding side of quadrilateral ABCD.

Q. 16.Construct a cyclic quadrilateral ABCD where AB = 3cm, BC = 6cm, CA = 4cm. and AD = 2cm, Also construct a quadrilateral similar to ABCD whose sides are 1.5 times the corresponding sides of ABCD.

Q. 17.Draw a line segment of length 10cm and divide it (i) internally and (ii) externally in the ration 3 : 4.