Question

given: ∠1 ≅ ∠2
prove: p || q
assemble the proof by dragging tiles to
the statements and reasons columns.
angles lines statements reasons
≅ ∠1 ∠2 ∠3
statements reasons

Explanation:

Step1: Identify Vertical Angles

$\angle 1$ and $\angle 3$ are vertical angles, so $\angle 1 \cong \angle 3$ (Vertical Angles Theorem).

Step2: Use Given Congruence

Given $\angle 1 \cong \angle 2$, by Transitive Property (if $\angle 1 \cong \angle 3$ and $\angle 1 \cong \angle 2$, then $\angle 2 \cong \angle 3$).

Step3: Conclude Parallel Lines

$\angle 2$ and $\angle 3$ are corresponding angles. If corresponding angles are congruent, then lines $p$ and $q$ are parallel (Corresponding Angles Converse).

Answer:

To prove \( p \parallel q \) given \( \angle 1 \cong \angle 2 \):

1. Statement 1: \( \angle 1 \cong \angle 3 \)

Reason 1: Vertical Angles Theorem (vertical angles are congruent).

1. Statement 2: \( \angle 1 \cong \angle 2 \)

Reason 2: Given.

1. Statement 3: \( \angle 2 \cong \angle 3 \)

Reason 3: Transitive Property of Congruence (if \( \angle 1 \cong \angle 3 \) and \( \angle 1 \cong \angle 2 \), then \( \angle 2 \cong \angle 3 \)).

1. Statement 4: \( p \parallel q \)

Reason 4: Corresponding Angles Converse (if corresponding angles are congruent, lines are parallel).

(Assemble the proof by dragging these statements/reasons into the table.)