Question

Kelly and Daniel wrote the following proofs to prove that vertical angles are congruent. Who is correct?

Kelly is correct, but Daniel is not.
Neither Kelly or Daniel is correct.
Daniel is correct, but Kelly is not.
Both Kelly and Daniel are correct.

Answer 1

Answer: B) Neither Kelly or Daniel is correct. 

A geometric proof is a series of logical reasonings that, starting from a hypothesis, lead to a thesis, using a sequence of statements, axioms, and theorems.

Looking at Kelly's proof, we can say that she is not right. Indeed, she uses the thesis, what she wants to prove, as a justification for her statements.

On the contrary, Daniel uses definitions and properties as a justification for his statements. Although, he does not use the correct justification for statements 1 and 2. Indeed, ∠1 + ∠2 = 180 because they are a linear pair, as well as ∠1 and ∠4.

A linear pair is a pair of adjacent angles formed when two lines intersect, while the supplementary angles definition states that two angles are supplementary when they add to 180 degrees without being necessary next to each other. Since Daniel does not know the effective measure of the angles, he cannot use the definition of supplementary angles.

Hence, neither Kelly or Daniel is correct.

Answer 2

Answer:

C.) Daniel is correct

Step-by-step explanation:

In Daniel's proof, he wrote down each angle that was vertical to the other. He was able to correctly write the statements and give the proper corresponding justification. Kelly, on the other hand, had only wrote down the theorem. She did not mention any properties or definitions to justify her proof, so she is incorrect. That leaves us with the answer choice, C.) Daniel is correct.