a We want to notice something about the angle formed at the top of the page by the folds. Measuring the angle with a protractor, we can see that it measures 90^(∘). Therefore, it is a right angle.
b A two-column proof lists each statement on the left column and its justification to its right. In this case, we can see that the four angles along the fold, which are ∠ 1, ∠ 1, ∠ 2, and ∠ 2, add up to 180^(∘), a straight angle. Therefore, using the Angle Addition Postulate we can write an equation connecting its measures.
m∠ 1+m∠ 1+m∠ 2+m∠ 2=180^(∘)
This is how we will begin our proof!
Stat. 1)& m∠ 1 + m∠ 1 + m∠ 2 + m∠ 2 = 180^(∘)
Reason 1)& Angle Addition PostulateNext, we can simplify the equation by combining like terms. Then, we will factor out 2. by using the Distributive Property.
We can list this as the next step in our proof.
Statement2)& 2(m∠ 1+m∠ 2)=180^(∘)
Reason2)& Distributive Property
Now, using the Division Property of Equality, we will divide both sides of the equation by 2.
2(m∠ 1+m∠ 2)=180^(∘)
⇕
m∠ 1+m∠ 2 =90^(∘)
This shows us that no matter how we make the folds, the sum of m∠ 1 and m∠ 2 is always a right angle. Therefore, this is the last step in our proof.
Statement3)& m∠ 1+m∠ 2=90^(∘)
Reason3)& Division Property of Equality
