construct an isosceles triangle ABC with base BC=6cm, AB=AC and angle A 90degree

Here are the steps of construction:

Step 1 : Make a line BC = 6 cm as base of the triangle.

Step 2 : AB = AC, so the angles at B and C will be same and we are given ∠A = 90°

∴ ∠B = ∠C = 45°

So, make an ∠XBC = 45° at point B.

Step 3 : Now, make an ∠YCB = 45° at point C.

Step 4: Name the point as A, where these two angles meet. (Clearly, ∠A = 90°).

Thus, ∆ABC is the required ∆.