CBSE Class 9 Answered

   Eg: Construct a triangle with base of length 7.5 cm, the difference of the other two sides 2.5 cm, and one base angle of 45°

          Given          : In ΔABC, base BC = 7.5 cm, the difference of the other two sides, AB – AC or AC – AB = 2.5 cm and one base angle is 45°.

          Required      : To construct the ΔABC,

          CASE (i) AB – AC = 2.5 cm.

          Steps of Construction:

1. Draw BC = 7.5 cm.
2. At B, construct angleCBX = 45°.
3. From BX, cut off BD = 2.5 cm.
4. Join CD.
5. Draw the perpendicular bisector RS of CD intersecting BX at a point A.
6. Join AC. Then, ABC is the required triangle.

CASE (ii) AC – AB = 2.5 cm

Steps of Construction:

1. Draw BC = 7.5 cm.
2. At B, construct angleCBX = 45° and produce XB to form a line XBX’.
3. From BX’, cut off BD’ = 2.5 cm.
4. Join CD’.
5. Draw perpendicular bisector RS of CD’ intersecting BX at a point A.