Question

If Line segment C B. bisects ∠ACD, what additional information could be used to prove ΔABC ≅ ΔDBC using SAS? Select three options.

m∠ABC = 125° and AB ≅ DB
ΔACD is isosceles with base AD
ΔABD is isosceles with base AD
CD = 52 cm
AB = 29 cm

Answer 1

Choose:
- m∠ABC = 125° and AB ≅ DB
- ΔACD is isosceles with base AD
- ΔABD is isosceles with base AD

Reason: CB bisects ∠ACD so ∠ACB = ∠BCD. To use SAS you need a pair of equal sides and the included equal angle plus the common side BC. ΔACD is isosceles (base AD) gives AC = DC. AB ≅ DB (either given directly in the first choice or implied by ΔABD being isosceles) gives AB = DB. With BC = BC (reflexive) and the angle equality from the bisector, these equalities allow congruence of ΔABC and ΔDBC by SAS.