Eden is cutting two triangular tiles for her bathroom. She needs the tiles to be congruent but is not sure she is cutting them that way. Eden has ensured that one side of both tiles is congruent. Which pair of sides would Eden need to compare in order to make sure the triangles are congruent by HL?

Question

Eden is cutting two triangular tiles for her bathroom. She needs the tiles to be congruent but is not sure she is cutting them that way. Eden has ensured that one side of both tiles is congruent. Which pair of sides would Eden need to compare in order to make sure the triangles are congruent by HL?

triangle ABC with coordinates A at 1 comma 4, B at 2 comma 4, C at 1 comma 1, and a right angle symbol at A and length of BC of 3 and 2 tenths units, triangle EFD with coordinates E at 2 comma negative 2, F at one comma negative 2, D at 2 comma 1 and a right angle symbol at E with length of FD of 3 and 2 tenths units

segment AC and segment FD
segment AB and segment EF
segment BC and segment EF
segment BC and segment FD

Answer 1

In order to determine if the triangles are congruent by HL (Hypotenuse-Leg), Eden would need to compare segment BC and segment FD. This is because the Hypotenuse-Leg congruence theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent. In this case, segment BC and segment FD are the hypotenuses of the two triangles.