=The statement used to prove angle B=angle C

Question

In the figure provided, precise measurements are given for the length of each side of △ABC.

If point D is on △ABC and AD¯¯¯¯¯¯¯¯ is constructed, determine the statement that could be used to prove that ∡B=∡C.

(1 point)

1. Point D is on AB¯¯¯¯¯¯¯¯ such that AD=6.1 and AD=BD. Since CD¯¯¯¯¯¯¯¯≅CD¯¯¯¯¯¯¯¯ by the side, side, side triangle congruence, △ACD≅△BCD and, therefore, ∠B≅∠C.
2. Point D is on BC¯¯¯¯¯¯¯¯,such that BD=6.1 and BD=CD. Since AD¯¯¯¯¯¯¯¯≅AD¯¯¯¯¯¯¯¯ by the side, side, side triangle congruence, △ABD≅△ACD and, therefore, ∠B≅∠C.
3. Point D is on AC¯¯¯¯¯¯¯¯ such that AD=5.95 and AD=CD. Since BD¯¯¯¯¯¯¯¯≅BD¯¯¯¯¯¯¯¯ by the side, side, side triangle congruence, △ABD≅△CBD and, therefore, ∠B≅∠C.
4. Point D is on AC¯¯¯¯¯¯¯¯ such that CD=5.95 and DA=DC. Since DB¯¯¯¯¯¯¯¯≅DB¯¯¯¯¯¯¯¯ by the side, side, side triangle congruence, △ADB≅△CDB and, therefore, ∠B≅∠C.

Answer 1

The answer is the second one (from above, but restated below), since line AB ≅ line AC (because both equal 11.9), and 6.1 is 1/2 of the length of line BC, which is 12.2:

Point D is on line BC, such that BD = 6.1 and BD = CD. Since line AD ≅ line AD by the side, side, side triangle congruence, △ABD ≅ △ACD, and, therefore, ∠B ≅ ∠C.