CBSE Class 9 Answered

Construction of a triangle, Given its Base, Difference of the Other Two Sides and one Base Angle.

          Example of both cases is shown as below. If in the question, the case is not clearly mentioned then you can do any one by letting the condition which you are depicting. However, if construction of right triangle is to be done where difference between hypotenuse and one side is given, then you know that hypotenuse is the longest side, so then do accordingly. 

        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.