Review the idea of a flow proof. Remember that arrows show the logical connections between the statements.
Practice makes perfect
Let's begin by reviewing the idea of a flow proof. Arrows show the logical connections between the statements. Reasons are written below the statements. We can begin our proof with the first given information, l ∥ n.
Statement1
l ∥ n
Given
Let's see what we can conclude from this while keeping in mind that we also know that ∠ 12 ≅ ∠ 8.
Statement2
∠ 4 ≅ ∠ 8
Corresponding Angles Theorem
The second piece of information we are given is that ∠ 12 ≅ ∠ 8. We will use it to continue our proof.
Statement3
∠ 12 ≅ ∠ 8
Given
Let's summarize what we know from the two last statements.
∠ 4 ≅ ∠ 8 and ∠ 8 ≅ ∠ 12
Now, by the Transitive Property of Congruence, we can conclude that ∠ 4 ≅ ∠ 12.
Statement4
∠ 4 ≅ ∠ 12
Transitive Property of Congruence
Notice that this statement follows from Statements 2 and 3. Thus, we will have two arrows that lead to Statement 4 in our flow proof. Let's continue!
As we can see, ∠ 4 and ∠ 12 are corresponding angles. We also proved that they are congruent. By the Converse of the Corresponding Angles Theorem, we can conclude that j ∥ k.
Statement5
j ∥ k
Converse of the Corresponding Angles Theorem
Final Proof
Combining everything from above, we can write our final proof.
&Given:l ∥ n, ∠ 12 ≅ ∠ 8
&Prove: j ∥ k
Proof:
