Five kinds of triangle

The figure shows triangle A B C. A B and A C each carry one tick, and B C carries two ticks. What kind of triangle is A B C? Five kinds of triangle, and each one has its own name. Right-angled. Acute-angled. Obtuse-angled. Equilateral. Isosceles. The first three are named by an angle. A small square says a corner is a right angle. An acute-angled triangle has all 3 of its angles under 90 degrees. An obtuse-angled one has a corner over 90 degrees, like this one hundred and twelve. The last two are named by their sides, and a tick is how a side says so. 3 ticks the same means 3 equal sides. That's equilateral, and every angle in it is 60 degrees. 2 ticks the same means 2 equal sides. That's isosceles. The two angles at the ends of its third side are its base angles, and the arcs say those two are equal. Marks are read in matching sets. Same mark, same length. Every side of this triangle carries a mark. But they are not all the same mark. A B and A C each carry one tick. Same mark, same length, so A B is equal to A C. B C carries two ticks. That's a different mark. A different mark means a different length, so B C isn't equal to either of them. Two equal sides. A B C is an isosceles triangle.

Your turn. The figure shows triangle G H J, with no marks on it. Nadia says that G H J is an isosceles triangle because G J and H J look the same length. Is Nadia right? Try it first. Pause if you like. G J and H J do look alike. But neither of them carries a tick, and nothing else on this triangle is marked either. Matching ticks would show equal sides here. Nadia cannot conclude that from the drawing. No. There is not enough information to say G H J is isosceles. Nothing on this triangle is marked. Matching ticks would show equal sides here. Two sides that look alike are still just two sides that look alike. A triangle's properties need evidence, not just appearance.