Question

A sequence of rigid transformations maps . Given and
, which additional congruence statement would be needed to prove the triangles are
congruent by the ASA Congruence Theorem?
Option #1:
Option #2:
Option #3:
Option #4:
(1 point)
△ABC → △A′′B′′C
′′ ∠C ≅∠C
′′
BC ≅
¯¯¯¯¯¯¯¯ B′′C′′ ¯¯¯¯¯¯¯¯¯¯¯¯
∠A ≅∠A′′
∠B ≅∠B′′
¯A
¯¯¯¯B
¯¯¯ ≅A′′B′′ ¯¯¯¯¯¯¯¯¯¯¯¯
AC ≅
¯¯¯¯¯¯¯¯ A′′C′′

Option # would be needed to prove the triangles are congruent by the ASA Congruence theorem

Answer 1

You need ∠B ≅ ∠B′′.

Reason: ASA requires two angles and the included side. With BC ≅ B′′C′′ and ∠C ≅ ∠C′′, the side BC is included between ∠B and ∠C, so you must have ∠B ≅ ∠B′′ to apply ASA.