Question

Diagonals of a square divide it into 4 congruent triangles. Are all these triangles congruent to each other? If yes, using which criterion?

Answer 1

Yes, diagonals of a square divide it into 4 congruent triangles. These triangles are congruent using RHS congruency rule.

In a square, diagonals intersect each other at right angles.

Therefore, the hypotenuse (AB, BC, CD, DA) of all the four triangles are equal as they are sides of the same square.

Also the diagonals in a square bisect each other, therefore AO=OB=OC=OD.

Hence the triangles are congruent using RHS congruency rule.