Question
Thu March 07, 2013 By:

# In Ex 11.2 Of This Chapter In Third question Why Did we Take 2cm Below the angle as in other questions we took the cms on the angles made??

Thu March 07, 2013
In the third question, the difference between two sides of the triangle is given and when the difference is given, two cases arise. The two are given below:

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.

To know more about contructions, you can go through the videos of this chapter available on our site.
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