Use the fact that ∠4 and ∠5 form a linear pair.
Statements
Reasons
1.
∠5 ≅ ∠6
1.
Given
2.
m∠5 = m∠6
2.
Definition of congruent angles
3.
m∠4 + m∠5 =180
3.
Supplement Theorem
4.
m∠4 + m∠6 =180
4.
Substitution Method
5.
∠4 and ∠6 are supplementary
5.
Definition of supplementary angles
Practice makes perfect
Let's begin by looking at the given information and what we want to prove.
Given:& ∠5 ≅ ∠6
Prove:& ∠4 and ∠6 are supplementaryLet's highlight the congruent parts in the given diagram.
Notice that ∠4 and ∠5 form a linear pair. With this information, we are ready to write a two-column proof.
