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 ≅ ∠6Now, 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.
