Construct an isos

Steps of construction:

i. Now in order to make a triangle, draw a line segment AB = 8 cm.

ii. Draw two arcs intersecting at 4 cm distance from points A and B; on either side of AB.
Join these arcs to get perpendicular bisector CD of AB. (Since, altitude is the perpendicular bisector of base of isosceles triangle).

iii. Join points A and B to C in order to get the triangle ABC.

iv. Now, draw a ray AX which is at an acute angle from point A.

As 

And 3 is greater between 3 and 2,

So

Plot 3 points on AX such that:

AA₁ = A₁A₂ = A₂A₃.

v. As 2 is smaller between 2 and 3. Join A₂ to point B.
Draw a line from A₃ which is parallel to A₂B meeting the extension of AB at B’. 

vi. Draw B’C’ || BC. Then, draw A’C’ || AC.

Triangle AB’C’ is the required triangle.

Justification:

We need to prove,



By construction



As C^'B^' || CB

They will maker equal angles with line AB.

∠ACB = ∠AC^'B^'     ..... (corresponding angles)

In ΔACB and ΔAC^'B^' 
∠A = ∠A  (common)
 ∠ACB = ∠AC^'B^'  (corresponding angles)

So ΔACB ∼ ΔAC^'B^' 

As corresponding sides of similar triangles are in ratio,

Hence,