Question

trishna wrote a paragraph proof to prove that alternate exterior angles, ∠a 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) trishna did not make a mistake. her proof is correct. the reason that m∠a = m∠e is because they are vertical angles, not corresponding angles. the reason that m∠e = m∠h is because they are a linear pair, not vertical angles. the reason that m∠a = m∠h is because they are corresponding angles, not because of the transitive property of equality. check answer remaining attempts : 3

Explanation:

1. Recall the definitions: Corresponding angles are in the same relative position with respect to the transversal and the parallel - lines, and vertical angles are opposite each other when two lines intersect.
2. Analyze Trishna's proof: $\angle A$ and $\angle E$ are indeed corresponding angles when $m\parallel n$, so the statement $m\angle A = m\angle E$ because they are corresponding angles is correct.
3. Analyze the relationship between $\angle E$ and $\angle H$: $\angle E$ and $\angle H$ are not vertical angles. Vertical angles are formed by the intersection of two lines. $\angle E$ and $\angle H$ are a linear - pair (adjacent and supplementary), not vertical angles.

Answer:

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