Question

If two triangles have the same area, they must be congruent.
True
False

Answer 1

Consider two right-angled triangles. One with base 1 and height 4. Another with base 2 and height 2.

The first one has area
= base x height / 2
= 1 x 4 / 2
= 2
and so does the second one,
= base x height / 2
= 2 x 2 / 2
= 2

So now, if two triangles have the same area, must they be congruent?

Answer 2

Draw a diagram of the two triangles I described. They have the same area. But are they congruent?