Question

Could triangle ABC be congruent to triangle ADC by SSS? Explain.

a.Yes but only if AB ~=DC
b.Yes but only if BC~= DC
c. No, because AB is not congruent to AC
d. No, Because AB ~= DA

Answer 1

yes, but only if BC ≅ DC.

Answer 2

Having a certain triangle there are some cases of congruency:
SSS (side side side) All three corresponding sides are equal in length.
SAS (side angle side) A pair of corresponding sides and the included angle are equal.
ASA (angle side angle)
AAS (angle angle side)

As we can observe there must be always 3 components of congruency. Triangle ABC can be congruent to triangle ADC by SSS if we have 3 sides that are equal. We already have two components: AB=AD and AC=AC (AC is a common side) so we need the third component BC=CD. The answer to your question is option B.