How to construct a triangle? Numerical Example.

Lets understand the construction of triangle with an example. Click on the link to Watch the VIDEO explanation: Watch Video

Construction of a Triangle, Given its Base. Difference of the Other Two Sides and One Base Angle
Problem : Construct a triangle with the base of length 7.5cm. The difference of the other two sides being 2.5 cm and one base angle of 45 degrees. 
Solution:
We are given the base BC is equal to 7.5 cm the difference of the other two sides, AB minus AC or AC minus AB is equal to 2.5 cm and one base angle of 45 degrees. It is required to construct the triangle ABC.
Case 1 AB minus AC is equal to 2.5 cm
Steps of construction
Draw a ray BX and cut off a line segment BC equal to 7.5 cm from it.
Construct angle YBC equal to 45 degrees.
Cut off a line segment BD is equal to 2.5 cm from BY.
Join CD.
Draw a perpendicular bisector RS of CD, intersecting BY at a point A.
Join AC.
ABC is the required triangle.

Case 2 AC minus AB is equal to 2.5 cm
Steps of construction
Draw a ray BX and cut off a line segment BC equal to 7.5 cm from it.
Construct a ray BY making an angle of 45 degrees with BC and produce YB to form a line YBY dash.
Cut off a line segment B dash D is equal to 2.5 cm from B.
Join CD dash.
Draw a perpendicular bisector RS of CD dash, intersecting BY at a point A.
Join AC.
ABC is the required triangle.