Exercise 38 Page 132

Given ∠ 1 and ∠ 2 are complementary. ∠ 3 and ∠ 4 are complementary. ∠ 2 ≅ ∠ 4 In our second step, we will use the Definition of Complementary Angles. The definition states that two angles are complementary if and only if the sum of the angles is equal to 90^(∘). Definition of Complementary Angles ∠ 1 +∠ 2=90 ∠ 3 + ∠ 4 = 90 Since both sum are equal to 90^(∘), we use the Transitive Property of Equality to write our next step. Transitive Property of Equality ∠ 1 +∠ 2 = ∠ 3 + ∠ 4 We have been also given that ∠ 2 is equal to ∠ 4. Thus, we can use the Substitution Property of Equality to substitute ∠ 2 for ∠4. Substitution Property of Equality ∠ 1 +∠ 2 = ∠ 3 + ∠ 2 Now, we will subtract ∠ 2 from both sides of the equation by using the Subtraction Property of Equality. Subtraction Property of Equality ∠ 1 = ∠ 3 Finally, we can complete our proof by the Definition of Congruent Segments. The definition states that two angles are congruent if and only if the have the same measure of angle. Definition of Congruent Segments ∠ 1 ≅ ∠ 3 Combining these steps, let's construct our two-column proof.