Question

proving a theorem a2) use the reason bank to prove the consecutive interior angles theorem. given p || q, and t as the transversal prove ∠1 and ∠2 are supplementary angles. two - column proof statements 1. p || q, and t as the transversal 2. ∠1 ≅ ∠3 3. m∠1 ≅ m∠3 4. m∠2 + m∠3 = 180° 5. m∠2 + m∠1 = 180° 6. ∠1 and ∠2 are supplementary angles. reasons 1. 2. 3. 4. 5. 6. reasons bank definition of supplementary angles substitution property of equality given linear pair postulate definition of congruent angles alternative interior angles theorem

Explanation:

Step1: Match given statement

The first statement is the given information, so the reason is "Given".

Step2: Identify congruent angles rule

$\angle1 \cong \angle3$ uses the Alternate Interior Angles Theorem (since $p \parallel q$).

Step3: Define congruent angles measure

Congruent angles have equal measures, so use the definition of congruent angles.

Step4: Linear pair angle sum

$\angle2$ and $\angle3$ form a linear pair, so their sum is $180^\circ$ (Linear Pair Postulate).

Step5: Substitute equal angle measures

Replace $m\angle3$ with $m\angle1$ using substitution property.

Step6: Define supplementary angles

Angles summing to $180^\circ$ are supplementary, use the definition.

Answer:

STATEMENTS	REASONS
2. $\angle1 \cong \angle3$	2. Alternate Interior Angles Theorem
3. $m\angle1 = m\angle3$	3. Definition of congruent angles
4. $m\angle2 + m\angle3 = 180^\circ$	4. Linear Pair Postulate
5. $m\angle2 + m\angle1 = 180^\circ$	5. Substitution Property of Equality
6. $\angle1$ and $\angle2$ are supplementary angles.	6. Definition of supplementary angles