Final answer:
To prove that angles LA and LC are equal, demonstrate that triangles ABD and CBD are congruent using the SSS postulate, and apply the CPCTC theorem to conclude that LA = LC.
Step-by-step explanation:
The question involves proving that angles LA and LC are equal given that segments AB and BC are equal as well as segments AD and CD. This proof is grounded in the principles of geometry, specifically the concept of congruent triangles. The hint suggests demonstrating that triangles ABD and CBD are congruent, which would imply that corresponding angles LA and LC are also congruent due to the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) theorem.
Since AB = BC and AD = CD by given information, and BD is common to both triangles ABD and CBD, we can conclude that the triangles are congruent by the Side-Side-Side (SSS) postulate. Thus, it follows that angle LA = angle LC because they are corresponding angles of congruent triangles ABD and CBD.