To prove the Transitive Property of Angle Congruence, we have to show that if ∠ 1 is congruent to ∠ 2 and ∠ 2 is congruent to ∠ 3, then ∠ 1 is congruent to ∠ 3. Remember that in a two-column proof we list each statement on the left and
its justification on the right. We will begin our proof with the given information.
Statement1) & ∠ 1 ≅ ∠ 2 and ∠ 2 ≅ ∠ 3
Reason1) & Given
Each statement of the proof must follow logically from its previous steps. Now, by the definition of congruent angles, if two angles are congruent then they have the same measure.
Statement2) & m∠ 1 = m∠ 2 and m∠ 2 = m∠ 3
Reason2) & Definition of congruent angles
By the Transitive Property of Equality, we can equate m∠ 1 and m∠ 3.
Statement3) & m∠ 1= m∠ 3
Reason3) & Transitive Property of Equality
Finally, by the definition of congruent angles, if two angles have the same measure then they are congruent.
Statement4) & ∠ 1 ≅ ∠ 3
Reason4) & Definition of congruent angles
Let's show this as a two-column proof.
