Construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11 cm

 


Steps of construction:


 


Step 1: A line segment PQ = 11cm is drawn. ( XY + YZ + ZX = 11cm)


 


Step 2: An angle RPQ = 300 is constructed at a point A and an angle SQP = 900 at point B.


 


Step 3: Angle RPQ and SQP are bisected. The bisectors of these angles intersect each other at point X.


 


Step 4: Perpendicular bisectors TU of PX and WV of QX are constructed.


 


Step 5: Let TU intersect PQ at Y and WV intersect PQ at Z. XY and ZY are joined.


 


Thus, Δ XYZ is the required triangle:



 

4