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Construction of a Triangle given its Base, Sum of the Other Two Sides and One Base Angle

Given : Base BC = x cm, AB + AC = y cm and

ABC = θ°, of triangle ABC.

Required : To construct a triangle ABC.

Steps of construction:
1. Draw a line BX and cut off a line segment BC = x cm from it.
2. Construct

XBY = θ°.
3. From BY cut off a line segment BD = y cm.
4. Join CD.
5. Draw the perpendicular bisector of CD, intersecting BD at a point A.
6. Join AC.
ABC is the required triangle.


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