What is the relation between ∠ 4 and ∠ 5? What about ∠ 6 and ∠ 7?
Statements
Reasons
1.
∠ 4 ≅ ∠ 7
1.
Given
2.
∠ 4 ≅ ∠ 5
2.
Vertical Angles Theorem
3.
∠ 5 ≅ ∠ 7
3.
Transitive Property of Congruence
4.
∠ 6 ≅ ∠ 7
4.
Vertical Angles Theorem
5.
∠ 5 ≅ ∠ 6
5.
Transitive Property of Congruence
Practice makes perfect
Let's begin by looking at the given information and what we want to prove.
Given:& ∠ 4 ≅ ∠ 7
Prove:& ∠ 5 ≅ ∠ 6
Now, let's highlight this information in the given diagram.
From the diagram, we can see that ∠ 4 and ∠ 5, as well as ∠ 6 and ∠ 7, are vertical angles. This is a key fact for the proof. Now, we can proceed with the two-column proof.
