∆ABC represents a randomly drawn triangle. ∆BCD is an isosceles triangle with sides BC and BD congruent. Point D lies on the line passing through points A and B. Use this information to answer the questions that follow. As the construction shows, the measure of ∠ACD is greater than the measure of ∠BCD. Based on this information, create an inequality involving sides AD and AC and explain your reasoning. Create a sum involving side lengths from ∆ABC that is equal to the length of line segment AD. Explain your reasoning. Create a sum involving side lengths from ∆ABC that is equal to the length of line segment AD. Explain your reasoning. Combine the answers from parts a and b to relate the side lengths of ∆ABC. What theorem does this construction and logic prove?