NCERT Class 9 Maths Solutions Chapter - 11 Constructions, Ex- 11.2

Ex - 11.2

Question 1.  Construct a triangle ABC in which BC = 7 cm, B = 75^o and AB + AC = 13 cm.

Solution

The steps of construction for the required triangles are as follows:

Step I: Draw a line segment BC of 7 cm. At point B draw an angle of 75^o sayXBC.  

Step II: Cut a line segment BD = 13 cm (that is equal to AB + AC) from the ray BX.  

Step III: Join DC and make an angle DCY equal to BDC  

Step IV: Let CY intersects BX at A. ABC is the required triangle.

Question 2.  Construct a triangle ABC in which BC = 8 cm, B = 45^o and AB - AC = 3.5 cm.

Solution

The steps of construction for the required triangles are as follows:
Step I: Draw the line segment BC = 8 cm and at point B make an angle of 45^o say XBC.   
Step II: Cut the line segment BD = 3.5 cm (equal to AB - AC) on ray BX.

Step III: Join DC and draw the perpendicular bisector PQ of DC.

Step IV: Let it intersect BX at point A. Join AC. ABC is the required triangle.

Question 3.  Construct a triangle PQR in which QR = 6 cm, Q = 60^o and PR - PQ = 2 cm

Solution

The steps of construction for the required triangles are as follows:
Step I: Draw line segment QR of 6 cm. At point Q draw an angle of 60^o say XQR.
Step II: Cut a line segment QS of 2 cm from the line segment QT extended an opposite side of line segment XQ. (As PR> PQ and PR - PQ = 2cm). Join SR.
Step III: Draw perpendicular bisector AB of line segment SR. Let it intersect QX at point P. Join PQ, PR. PQR is the required triangle.

Question 4.  Construct a triangle XYZ in which Y = 30^o, Z = 90^o and XY + YZ + ZX = 11 cm

Solution

The steps of construction for the required triangles are as follows:

Step I: Draw a line segment AB of 11 cm.(As XY + YZ + ZX = 11 cm)

Step II: Construct an angle PAB of 30^o at point A and an angle QBA of 90^o at point B.

Step III: Bisect PAB and QBA. Let these bisectors intersect each other at point X.

Step IV: Draw perpendicular bisector ST of AX and UV of BX. Step V: Let ST intersects AB at Y and UV intersects AB at Z.Join XY, XZ.XYZ is the required triangle.

Question 5.  Construct a right triangle whose base is 12 cm and sum of its hypotenuse and other side is 18 cm.

Solution

The steps of construction for the required triangles are as follows:
Step I: Draw line segment AB of 12 cm. Draw a ray AX making 90^o with AB.

Step II: Cut a line segment AD of 18 cm. (As sum of other two side is 18) from ray AX.

Step III: Join DB and make an angle DBY equal to ADB.

Step IV: Let BY intersects AX at C. Join AC, BC.ABC is the required triangle.

Ex-11.1

Ex-12.1