Construct ∆ABC in which BC = 7 cm, ∠B = 75° and AB + AC = 12 m.

Given: base BC = 7cm, AB + AC = 12 cm and

∠B = 75° of Δ ABC.

Required: To construct a ΔABC

Steps of construction:

Step 1: Draw a segment BC of length of 7 c

Step 2: At vertex B, construct ∠B = 75° and produce a ray BP.

Step 3: Mark an arc on ray BP cutting at D such that BD = 12cm.

Step 4: Draw segment CD.

Step 5: Construct the perpendicular bisector of segment CD.

Step 6: Name the point of intersection of ray BP and the perpendicular bisector of CD as A.

Step 7: Draw segment AB.

ΔABC is the required triangle.