Question

in triangle XYZ, angle X = 50°, XY = 4.2 cm, XZ = 3.6 cm. construct triangle XYZ. also construct triangle XMN such that XY/ XM = 4/5 and triangle XYZ ~ triangle XMN.

Answer 1

Steps of construction:-

• Draw a line of 4.2 cm and name it as XY .

• Taking X as center make an angle of 50° , and extend it . Now taking X as center cut an arc of 3.6 cm and name it as XZ . Also join Y to Z forming ΔXYZ .  

• Now extend a line from X as shown in fig and cut each arc of any measurement (I have randomly take 1.2 cm) , cut 6 segments and name them as A1  , A2 , A3 … and so on till A6 .

• Join Y to A4 and taking A5 construct a parallel A5 M .

• Again construct a parallel of YZ to MN . Join M and N forming MN.  

Hence ΔXMN~ΔXYZ