geometry proofs

Question

Given: <DCA is congruent to <BCA, <B is congruent to <D

Prove: segment AB is congruent to segment AD

Answer 1

Hello Hannah,

Is there a drawing with the problem, from which I can assume <B is the same as saying <CBA,

and <D is the same as angle <CDA?

If that is true, here is the proof:

S1) <DCA ≅ <BCA R1) Given

S2) <B ≅ <D R2) Given

S3) Seg(AC) ≅ Seg(AC) R3) Reflexive Property

S4) ΔCDA ≅ ΔCBA R4) AAS

S5) Seg(AB) ≅Seg(AD) R5) CPCTC

Thank you for the question, and have a great evening!

Michael Ehlers