Two angles are complementary if their combined measure is 90^(∘).
See solution.
Practice makes perfect
Let's begin by looking at the given information and what we want to prove.
Given:& ∠1 is a complement of ∠2.
& ∠2 ≅ ∠ 3
Prove:& ∠ 1 is a complement of ∠ 3.
Now, let's take a look at the statements and reasons that need to be completed one at a time.
Blank 2
From the information given, we already know that ∠ 2 ≅ ∠ 3. Therefore, on the second row we should fill out Given.
&S2. ∠ 2 ≅ ∠ 3
&R2. Given
Blank 3
The given information, that ∠ 1 and ∠ 2 are complementary, means that the sum of their measures equals 90^(∘). We write this by using the definition of complementary angles.
&S3. m∠ 1+m∠ 2 =90^(∘)
&R3. Definition of complementary angles
Blank 5
We want to prove that ∠ 1 is a complement angle of ∠ 3. Since we know that m∠ 2= m∠ 3, we can perform this substitution on the equation on the third row, which leaves us with an equation describing the sum of m∠ 1 and m∠ 3.
m∠ 1+ m∠ 2=90^(∘)
⇓
m∠ 1+ m∠ 3=90^(∘)
With this information, we can fill in the blank on the fifth row.
&S5. m∠ 1+m∠ 3=90^(∘)
&R5. Substitution Property of Equality
Blank 6
Knowing that m∠ 1 and m∠ 3 equals 90^(∘), we can finally by the definition of complementary angles claim that ∠ 1 is a complement of ∠ 3.
&S6. ∠ 1 is a complement of ∠ 3
&R6. Definition of complementary angles
Let's complete the two-column proof.
