Question

given: $overline{jk}paralleloverline{lm}$
prove: $angle1congangle8$

statement	justification

|2. $angle1congangle4$|2.
|3. $angle4congangle8$|3.
|4. $angle1congangle8$|4.
transitive property of equality
corresponding angles theorem
vertical angles theorem
substitution property of equality

Explanation:

Step1: Identify angle - pair relationship for ∠1 and ∠4

Since $\overline{JK}\parallel\overline{LM}$, ∠1 and ∠4 are corresponding angles. By the Corresponding Angles Theorem, when two parallel lines are cut by a transversal, corresponding angles are congruent. So the justification for ∠1≅∠4 is the Corresponding Angles Theorem.

Step2: Identify angle - pair relationship for ∠4 and ∠8

∠4 and ∠8 are vertical angles. By the Vertical Angles Theorem, vertical angles are congruent. So the justification for ∠4≅∠8 is the Vertical Angles Theorem.

Step3: Prove ∠1≅∠8

Since ∠1≅∠4 and ∠4≅∠8, by the Transitive Property of Equality (if a = b and b = c, then a = c for congruent angles), we can conclude that ∠1≅∠8. The justification for ∠1≅∠8 is the Transitive Property of Equality.

Answer:

1. Corresponding Angles Theorem
2. Vertical Angles Theorem
3. Transitive Property of Equality