Figure-8 triangle law

The two triangles in the horoscope have a pair of opposite corners that know each other. Because the diagonal is equal, the diagonal pair must be equal.

But the other two diagonal lines of these two triangles are not necessarily equal. Only when these two triangles are similar will there be a conclusion that the three angles are equal and corresponding.

A common case where three angles are equal is that the opposite groups of the top corners are parallel lines. According to the fact that the staggered angles in parallel lines are equal, the other two diagonal groups can be made equal respectively; On the other hand, if the four points on the outside of the figure 8 are on the same circle, the other two diagonal groups can be made equal by using the theorem of circumferential angle. However, it should be noted that the two sets of diagonals referred to in these two cases are different diagonal groups.

Generally speaking, the top angles of eight characters must be equal, but the diagonal lines are not necessarily equal.