Question

if cd bisects ∠acd, what additional information could be used to prove △abc≅△dbc using sas? select three options.
□m∠abc = 125° and ab = db
□△acd is isosceles with base ad
□△abd is isosceles with base ad
□cd = 52 cm
□ab = 29 cm

Explanation:

To prove △ABC ≅ △DBC by SAS, we need two sides and their included angle congruent. CB bisects ∠ACD, so ∠ACB ≅ ∠DCB (included angle). For SAS:

• If AC=DC, then with CB=CB (common), SAS holds. △ACD isosceles with base AD implies AC=DC (legs). CD=52 cm (AC=52 cm, given) also implies AC=DC.
• If AB=DB and ∠ABC=∠DBC, with CB=CB, SAS holds. m∠ABC=125° and AB≅DB provides AB=DB and the included angle.

Answer:

A. m∠ABC = 125° and AB ≅ DB, B. △ACD is isosceles with base AD, D. CD = 52 cm