Constructions Test - 6

To construct a triangle , we need measurements of its base, base angle and sum or difference of other two sides i.e to construct a △ABC, we need BC, ∠B and AB-AC or AB+AC.

As we know that the the altitude of an equilateral triangle is given as √3/4(side)2. 

If the altitude of equilateral triangle is given then we can determine its side by using above formula and further construct it.

To construct a △ABC whose base BC = 10cm, base angle ∠B = 60⁰ and sum of other two sides i.e. AB+AC=14 cms are given, we draw a ray of angle 60⁰ from initial point of base i.e. B and draw an arc of length equal to the sum of other two sides i.e. 14 cm. The line segment thus formed is named as BD which is of length 14 cm.

With the help of a ruler and a compass, we can not construct an angle which is not a multiple of 15⁰ and as we know 50⁰is not a multiple of 15⁰,so, we can't construct it.

To construct a △ABC, whose, base BC=3 cm, base angle ∠C = 30⁰ and sum of other two sides i.e. AB + AC is given, the sum of other two sides should be more than its base i.e. AB+AC should be greater than BC. 

As 3.2>3, so , we can construct the △ABC.