Construct an isosceles triangle such that the vertex angle a

Construct an isosceles triangle such that the vertex angle and the sum of the equal sides have being given. Given triangles triangle ABC and triangle DEF such that AB bar approximatelyequalto DE bar, AC bar approximatelyequalto DF bar and angle A > angle D, prove that BC > EF.

Solution

Using theorem : side opposite to greatest angle is greatest, we can conclude that since angle A is greater than angle D and because length of AB = length of DF and length of AC = Length of DE therefore length of BC which is opposite to angle A should be greater than length of EF which is opposite to angle D.