Let's begin by looking at the given information and the desired outcome of the proof. Then, we can write a paragraph proof!
&Given ∠ 1 is a right angle.
&Prove ∠ 2 is a right angle.
By the definition of a right angle, ∠ 1 measures 90^(∘).
By the Substitution Property of Equality, 90^(∘)+m∠ 2 =180^(∘).
Then, using the Subtraction Property of Equality, we can find the measure of ∠ 2.
90^(∘)+m∠ 2=180^(∘)
⇕
m∠ 2 = 90^(∘)
We conclude that ∠ 2 measures 90^(∘).
By the Subtraction Property of Equality, m∠ 2=90^(∘).
Since m∠ 2=90^(∘), by the definition of right angle, we know that ∠ 2 is a right angle.
By the definition of right angle, ∠ 2 is a right angle.
Completed Proof
Considering the given information, we can summarize all the steps in a paragraph proof.
&Given ∠ 1 is a right angle.
&Prove ∠ 2 is a right angle.
Proof. By the definition of a right angle m∠ 1 = 90^(∘). Since ∠ 1 and ∠ 2 form a linear pair, by the Linear Pair Postulate they are supplementary angles. Then, by the definition of supplementary angles m∠ 1 + m∠ 2 = 180^(∘). By the Substitution Property of Equality 90^(∘) + m∠ 2 = 180^(∘). Then m∠ 2 = 90^(∘) by the Subtraction Property of Equality. Finally ∠ 2 is a right angle by the definition of a right angle.
