Arnav knows that (3,4,5) and (5,12,13) are pythagorean triples. He wants to show that (15,20,25) is also a pythagorean triple. Besides using the converse of the pythagorean theorem, is there another way Arnav can show that (15,20,25) is a pythagorean triple?

Arnav can use the fact that scaling doesn't affect the angles of a triangle, and that (3,4,5) is already stated being a Pythagorean triple.

What are similar figures?

Similar figure are zoomed in or zoomed out (or just no zoom) version of each other. They are scaled version of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.

So, if a side of a figure is of length L units, and that of its similar figure is of M units, then:

M = k × L units

where 'k' will be called as scale factor.

The linear things grow linearly like length, height etc.

We're given that:

(3,4,5) is a pythagorean triple.

Let ABC be a right angled triangle possessing those sides (as the side lengths of a right angled triangle form pythagorean triple).

Scale each side of ABC by scale factor of 5, then we get:

(15, 20, 25) as a triple.

When scaling a figure, angles in it doesn't change because of angle being a relative quantity, not depending on the length of sides, but on the degree of rotation between two sides, which is unaffected because of scaling.

That means, that right angled triangle ABC, when scaled is still right angled triangle (because of its one of the angle 90 degrees still being 90 degrees in the new scaled triangle), but its sides are (15,20,25).

Now, since the triple (15,20,25) is side lengths of a right angled triangle, therefore, it is a pythagorean triple.

Thus, arnav can use the fact that scaling doesn't affect the angles of a triangle, and that (3,4,5) is already stated being a Pythagorean triple.

Learn more about scale factor here:

https://brainly.com/question/8765466