Question
Sun March 03, 2013

# URGENT QUERY

Sun March 03, 2013

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 45Ã‚Â°

Given          : In ÃŽÂ”ABC, base BC = 7.5 cm, the difference of the other two sides, AB Ã¢Â€Â“ AC or AC Ã¢Â€Â“ AB = 2.5 cm and one base angle is 45Ã‚Â°.

Required      : To construct the ÃŽÂ”ABC,

CASE (i) AB Ã¢Â€Â“ AC = 2.5 cm.

Steps of Construction:

1. Draw BC = 7.5 cm.
2. At B, construct angleCBX = 45Ã‚Â°.
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 Ã¢Â€Â“ AB = 2.5 cm

Steps of Construction:

1. Draw BC = 7.5 cm.
2. At B, construct angleCBX = 45Ã‚Â° and produce XB to form a line XBXÃ¢Â€Â™.
3. From BXÃ¢Â€Â™, cut off BDÃ¢Â€Â™ = 2.5 cm.
4. Join CDÃ¢Â€Â™.
5. Draw perpendicular bisector RS of CDÃ¢Â€Â™ intersecting BX at a point A.
Join AC. Then, ABC is the required triangle.

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