Geometry: Construction-Triangle when its base and vertical angle are given

Geometric Construction: Triangle when its base and vertical angle are given

Steps:-
 Step I: Draw a line segment equal to the base say BC of the triangle. Step II: Below BC, make an angle CBP equal to the vertical angle of the given triangle. Step III: Draw a line BE BP at the point B. Step IV: Draw the right bisector of  BC meeting a line BE BP at O. Step V: With O as the centre and OB as radius, draw a circle. Step VI: Take any point A on the circumference of the circle on the same side on which O lies. Step VII: Join AB and AC.
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Example: Construct a triangle with BC = 5.6 cm and vertex A such that mBAC = 60 . How many such triangles are possible?
 Solution: Steps of Construction Step I: Draw a line segment BC = 5.6 cm. Step II: Below BC, make CBP = BAC = 60 Step III: Draw BE BP at the point B. Step IV: Draw the right bisector QR of BC. Suppose QR meets BE at O. Step V: With O as centre and OB as radius, draw a circle. Step VI: Take any point A on the circumference of the circle on the same side on which O lies. Step VII: Join AB and AC. As any position on the arc BAC can be assumed, so there can be infinitely many such triangles.

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