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

segment BC and segment FD

Explanation:

In the lesson

Answer 2

The correct option is 2.

Explanation:

Given information: A(1,4), B(2,4), C(1,1), E(2,-2), F(1,-2), D(2,1). ∠A=∠E=90° and BC=FD=3 and 2 tenths units.

According to HL postulate, two triangles are congruent if their hypotenuse and corresponding one leg are congruent.

If ∠A=90° it means opposite side of A is hypotenuse. So, BC is hypotenuse.

If ∠E=90° it means opposite side of E is hypotenuse. So, FD is hypotenuse.

It is given that BC=FD=3 and 2 tenths units. It means hypotenuse are equal.

In triangles ABC and EFD, sides AB, BC and AC and corresponding sides of EF, FD and ED.

Triangles ABC and EFD are congurent by HL postulate if
`AB\cong EF` or
`AC\cong ED`.

Therefore the correct option is 2.