Trishna wrote a paragraph proof to prove that alternate exterior angles, ∠A

Question

and ∠H
, are congruent.

I am given that m∥n
. I know that m∠A=m∠E
because they are corresponding angles. I also know that m∠E=m∠H
because they are vertical angles. With this information, I can use the Transitive Property of Equality to write that m∠A=m∠H
. By the definition of congruence, ∠A≅∠H
and I have proven that alternate exterior angles are congruent.

What mistake did Trishna make?

(1 point)
Responses

The reason that m∠A=m∠H
is because they are corresponding angles, not because of the Transitive Property of Equality.
The reason that m∠A=m∠H
is because they are corresponding angles, not because of the Transitive Property of Equality.

The reason that m∠E=m∠H
is because they are a linear pair, not vertical angles.
The reason that m∠E=m∠H
is because they are a linear pair, not vertical angles.

The reason that m∠A=m∠E
is because they are vertical angles, not corresponding angles.
The reason that m∠A=m∠E
is because they are vertical angles, not corresponding angles.

Trishna did not make a mistake. Her proof is correct.

Answer 1

Trishna made a mistake in her reasoning regarding the angles involved in the proof. Specifically, the incorrect statement is:

The reason that m∠E=m∠H is because they are a linear pair, not vertical angles.

This is because ∠E and ∠H are vertical angles, which means they are congruent (m∠E = m∠H), not necessarily because they form a linear pair. Therefore, the correct explanation for m∠E = m∠H is based on the fact that vertical angles are congruent, rather than forming a linear pair.

So the correct response is:

The reason that m∠E=m∠H is because they are a linear pair, not vertical angles.