Triangles ABC and DEF are both right triangles. Each has a hypotenuse length of 10 m. Is this enough information to conclude that the two triangles are congruent?
5 years ago
Answered By Emily H
No, this isn't enough information to say that they are congruent. If they were congruent, then the ratio between the hypotenuse and either adjacent side would be the same for both triangles. As we only know the hypotenuse length and that it is a right triangle, there isn't enough information to make that conclusion without at least one other piece of information.
To illustrate this point, consider that you could have one triangle with side lengths of 6m, 8m, and 10m, and the other could have sides of 3.85m, 9.23m, and 10m, which both satisfy the conditions but are clearly not congruent.
5 years ago
Answered By Emily H
No, this isn't enough information to say that they are congruent. If they were congruent, then the ratio between the hypotenuse and either adjacent side would be the same for both triangles. As we only know the hypotenuse length and that it is a right triangle, there isn't enough information to make that conclusion without at least one other piece of information.
To illustrate this point, consider that you could have one triangle with side lengths of 6m, 8m, and 10m, and the other could have sides of 3.85m, 9.23m, and 10m, which both satisfy the conditions but are clearly not congruent.