Question

State the number of pairs of congruent triangles formed in a parallelogram when both its diagonals are drawn.

Answer 1

The shaded triangle in (1) and (2) are conguent. (2) and (4) are congruent.

The shaded triangle in (5) , (6) , (7) , (8) are congruent to each other.

so, number of pairs these make

= number of ways of selecting 2 out of 4

= $4_{C_2}$

= 6

$\therefore$ total number of ways $= 2+6 = 8$ pairs.