Exercise 42 Page 593

Let's consider the given diagram, hypothesis, and thesis. Given:& △ ABC, exterior ∠ BCD Prove:& m∠ A+m∠ B=m∠ BCD

According to the Triangle Sum Theorem, the sum of the measures of the three interior angles of a triangle add to 180^(∘). Triangle Sum Theorem m∠ A+m∠ B+m∠ BCA=180^(∘) If we look at the diagram, we can see that ∠ BCA and ∠ BCD form a linear pair. According to the Linear Pair Postulate, the measures of two angles that form a linear pair add to 180^(∘). Linear Pair Postulate m∠ BCD+m∠ BCA=180^(∘) By the Transitive Property of Equality, if two expressions equal 180^(∘), then they are equal. Transitive Property of Equality m∠ BCD+m∠ BCA = m∠ A+m∠ B+m∠ BCA By the Subtraction Property of Equality, we can subtract m∠ BCA from both sides to obtain an equivalent equation. Subtraction Property of Equality m∠ BCD = m∠ A+m∠ B ⇕ m∠ A+m∠ B=m∠ BCD We can summarize our proof using a table.