Question

1. if two triangles have the same area, what additional information is needed to show that they are congruent? one triangles altitude is congruent to the other triangles altitude. the triangles each have a right angle. one triangle has two angles that are congruent to two angles of the other triangle. the triangles are both isosceles.

Explanation:

Congruent triangles have equal corresponding sides and angles. For two triangles with the same area, having congruent altitudes is not enough. Having two - angle - congruence (by the Angle - Angle (AA) similarity criterion, but for congruence we need more) or being isosceles or having right - angles alone is not sufficient. We need a side - length congruence in addition to equal areas or altitudes or angle - congruences. The Angle - Angle - Side (AAS), Side - Angle - Side (SAS), Side - Side - Side (SSS), Hypotenuse - Leg (HL) (for right - triangles) are the congruence criteria. If one triangle's altitude is congruent to the other's altitude and the bases corresponding to those altitudes are also congruent, then the triangles are congruent.

Answer:

No option given provides sufficient additional information to show the triangles are congruent.