Question

Divide a square sheet in two triangles of equal area so that they are congruent.

Answer 1

∆ABC of = 1/2 x BC x AB

= 1/2 x 4 x 4 

= 8 sq unit

and area of ∆DCA

=  x DC x DA

=  x 4 x 4 = 8 sq unit

∴ Area of ∆ABC = Area of ∆CDA

In ∆ABC and ∆CDA

AB = CD, ∠B =∠D and AC = AC (common)

∴ By RHS rule of congruency, ∆ABC ≅ ∆CDA