Construct an isosceles triangle whose base is 8cm and altitude 4cm and then another triangle whose sides are times the corresponding sides of the isosceles triangle.

Let, ABR is a isosceles triangle

AR=RB

AB= 8 cm

AO is altitude of 4 cm

Step1: Draw a line segment AB= 8 cm

Bisect it, we get point O on AB

Step2: Taking O as a center, draw an arc of 4 cm radius , we get point R .

Step3: Draw a ray AS, making an acute angle with AB.

Step4: Locate 3 points A1,A2,A3.

Where, AA1=AA2, AA2=AA3

Step5: Join BA2

Draw a parallel line to BA2 ,which meets at B’ with A3. Draw a line parallel to BR intersecting the extended segment at R’

∆AB' R' is required triangle .

Justification

In ∆ABR and ∆AB' R'

∠ABR=∠AB'R' (Corresponding angle )

∠BAR=∠B'AR' (Common)

∴∆ABR~∆AB' R'

In ∆AA2B and ∆AA3B'

∠A2AB=∠A3AB'

∠AA2B=∠AA3B'

∴∆AA2B ~∆AA3B'

By comparison