How do you construct a congruent angle?

Answer 1

We know two triangles are congruent if and only if all of their sides are equal.

So that's the best way to do it. Pick a triangle you want to copy, on the side, draw a beam (one end extends infinitely sort), let the centre of your beam be point a.

Then use your compass to measure one of the triangle's side length by moving it from one endpoint to the other, then without changing the width of the compass, set the pointer at the point a and use the pen side draw a small arc. The intersection between the arc and the beam, we will call it point b.

Now measure another side of the triangle using the compass, and draw an arc from a. We will call this arc arc A.

Do the same for the remaining side of the triangle and draw an arc from point b, we will call this arc arc B.

The point if intersection of arc A and B we will call it c.

Triangle abc should be congruent to the original triangle.

Note: If you do it by hand (likely), it will not be perfect due to human and environmental errors.