if two triangles have equal areas then the two triangles will be congruent.
It is true that all congruent triangles have equal area.
But, it is not necessary that triangles having equal area will be congruent to one another they may or may not be congruent.
For eg., [ example for non-congruent triangles having equal areas]
(1) ABC has base BC = 6 cm and height AD = 4 cm, other sides AB =12 cm, CA = 17 cm.
ar (ABC) = 1/2 x 4 x 6 = 12 cm2.
(2) PQR has base QR = 8 cm and height PM = 3 cm, other sides PQ = 9 cm, RP = 10 cm.
ar (PQR) = 1/2 x 8 x 3 = 12 cm2.
Note that these two triangles ABC & PQR have equal area of 12 cm2 but from the measurements of the sides of both of the triangles, we know that they are not congruent.
But, at the same time triangles [not the above ones] , with same areas can be congruent.
: )
But, it is not necessary that triangles having equal area will be congruent to one another they may or may not be congruent.
For eg., [ example for non-congruent triangles having equal areas]
(1) ABC has base BC = 6 cm and height AD = 4 cm, other sides AB =12 cm, CA = 17 cm.
ar (ABC) = 1/2 x 4 x 6 = 12 cm2.
(2) PQR has base QR = 8 cm and height PM = 3 cm, other sides PQ = 9 cm, RP = 10 cm.
ar (PQR) = 1/2 x 8 x 3 = 12 cm2.
Note that these two triangles ABC & PQR have equal area of 12 cm2 but from the measurements of the sides of both of the triangles, we know that they are not congruent.
But, at the same time triangles [not the above ones] , with same areas can be congruent.
: )
