A two-column proof of the statement “The sum of the interior angles of any triangle is 180∘” is provided below. Rewrite this proof in paragraph form.
1. Draw line DE through A parallel to BC. (Construction)
2. ∠DAB=∠ABC. (Alternate interior angles)
3. ∠CAE=∠ACB. (Alternate interior angles)
4. ∠DAB+∠BAC+∠CAE=180∘. (Linear pair axiom)
5. Therefore ∠ABC+∠BAC+∠ACB=180∘. (Substitution)
Answer the following:
a. (i) Convert the two-column proof above into a coherent paragraph proof, including the headings ‘Given’, ‘To Prove’, ‘Proof’, and ‘Conclusion’.
b. (ii) Identify the exact step in your paragraph proof where Euclid’s parallel postulate is first invoked.
c. (iii) State the final result proved about the interior angles of a triangle.