Question

Write the process of Construction of a triangle when the base, a base angle and the difference between the other two sides of the triangle are given.

Answer 1

In ΔABC, given BC = 'a' cm, ∠B = x° and difference of two sides AB and AC is equal to 'b' cm. 

Case I: AB > AC 

Step 1: Draw the base BC = 'a' cm. 

Step 2: Make ∠XBC = x°. 

Step 3: Mark a point D on ray BX such that BD = 'b' cm. 

Step 4: Join DC. 

Step 5: Draw the perpendicular bisector of DC such that, it intersects the ray BX at a point A. 

Step 6: Join AC. 

Thus, ABC is the required triangle.

Case II: AB < AC 

Step 1: Draw the base BC = 'a' cm. 

Step 2: Make ∠XBC = x° and extend ray BX in the opposite direction. 

Step 3: Mark a point D on the extended ray BX such that BD = 'b' cm. 

Step 4: Join DC. 

Step 5: Draw the perpendicular bisector of DC such that, it intersects the ray BX at a point A.

Step 6: Join AC. 

Thus, ABC is the required triangle.