Question

write a two - column proof. given: ℓ∥m, ∠1≅∠2 prove: a∥b geometry chapter 3 resource book

Explanation:

Step1: Identify corresponding - angles

Since $\ell\parallel m$, $\angle1$ and $\angle3$ are corresponding angles, so $\angle1\cong\angle3$ (Corresponding - Angles Postulate).

Step2: Identify vertical - angles

$\angle2$ and $\angle3$ are vertical angles, so $\angle2\cong\angle3$ (Vertical Angles Theorem).

Step3: Use the Transitive Property

Since $\angle1\cong\angle3$ and $\angle2\cong\angle3$, by the Transitive Property of Congruence, $\angle1\cong\angle2$. Then, since $\angle1$ and $\angle2$ are corresponding angles formed by lines $a$ and $b$ with a transversal, $a\parallel b$ (Converse of the Corresponding - Angles Postulate).

Answer:

The two - column proof is as follows:

Statements	Reasons
2. $\angle1\cong\angle3$	Corresponding - Angles Postulate
3. $\angle2\cong\angle3$	Vertical Angles Theorem
4. $\angle1\cong\angle2$	Transitive Property of Congruence
5. $a\parallel b$	Converse of the Corresponding - Angles Postulate