How many different (mutually non-congruent) trapeziums can be constructed using four distinct side lengths from the set $\{1, 2, 3, 4, 5, 6\}$?

Suppose $BC$ is a given line segment in the plane and $T$ is a scalene triangle. The number of points $A$ in the plane such that the triangle with vertices $A, B, C$ (in that order) is similar to triangle $T$ is

If there are $m$ parallel lines in each of the two sets of parallel lines that form a parallelogram,then the total number of parallelograms formed is:

The number of diagonals in a polygon of $m$ sides is

In a plane,there are $37$ straight lines,of which $13$ pass through the point $A$ and $11$ pass through the point $B$. Besides,no three lines pass through one point,no line passes through both points $A$ and $B$,and no two lines are parallel. The number of intersection points the lines have is equal to:

Let $l_1$ and $l_2$ be two lines intersecting at $P$. If $A_1, B_1, C_1$ are points on $l_1$,and $A_2, B_2, C_2, D_2, E_2$ are points on $l_2$,and if none of these points coincides with $P$,then the number of triangles formed by these eight points is: