Question

1. in the figure, lines a and b are intersected by line t.

lauren says “a || b because m∠1 + m∠2 = 180”
kadeem says “a || b because ∠3 ≅ ∠2”
santiago says “a || b because ∠2 ≅ ∠4”
janiya says “a || b because ∠4 ≅ ∠1”
john says “a || b because ∠3 and ∠4 are supplementary”
who is(are) and explain why? select all that apply.

Explanation:

1. Lauren: $\angle1$ and $\angle2$ are a linear - pair. If $\angle1+\angle2 = 180^{\circ}$, it doesn't prove $a\parallel b$. A linear - pair of angles are supplementary regardless of whether the lines are parallel or not.
2. Kadeem: Similar to Lauren's case, $\angle1+\angle2 = 180^{\circ}$ due to being a linear - pair and not a proof of parallel lines.
3. Santiago: $\angle3$ and $\angle2$ are alternate interior angles. If $\angle3\cong\angle2$, then by the Alternate Interior Angles Theorem, $a\parallel b$.
4. Janiya: $\angle4$ and $\angle1$ are corresponding angles. If $\angle4\cong\angle1$, then by the Corresponding Angles Postulate, $a\parallel b$.
5. John: $\angle3$ and $\angle4$ are adjacent angles, and their supplementary relationship doesn't prove $a\parallel b$.

Answer:

Santiago, Janiya