Question

1. what changes would you make to turn this formal proof into a paragraph proof?

given: angles a and 15 are complementary.
prove: a = 75 degrees.
proof:

statements	reason
m∠a + 15 = 90	definition of complementary angles
m∠a = 75	by subtraction

○ leave out the reasons and just write the statements.
○ leave out all symbols and write out the words.
○ write the reasons first and then the statements.
○ write the statements and reasons in sentence format.

Explanation:

To convert a formal proof (with statements and reasons in a table) to a paragraph proof, we need to integrate both statements and their corresponding reasons into coherent sentences. Let's analyze each option:

• "Leave out the reasons and just write the statements": A paragraph proof still needs to explain the logic (reasons), so this is incorrect.
• "Leave out all symbols and write out the words": While symbols can be written as words, the key is integrating statements and reasons, not just removing symbols. This is not the main change.
• "Write the reasons first and then the statements": The order isn't the main issue; it's about combining them into sentences, not reordering.
• "Write the statements and reasons in sentence format": A paragraph proof presents the proof as a continuous paragraph, where each step (statement) is explained with its reason in sentence form. This matches the requirement.

Answer:

D. Write the statements and reasons in sentence format.