Question

Match the reasons to the statements in the proof. Given: m 1 + m 5 = 180° m 1 + m 4 = 180° Prove: | | 1. m∠1 + m∠5 = 180° and m∠1 + m∠4=180° Subtraction property of equality 2. m∠1 + m∠5 = m∠1 + m∠4 Substitution 3. m∠5 = m∠4 If alternate interior angles equal, then lines are ||. 4. is parallel to Given

Answer 1

In the given proof, we match the reasons to the statements. The first match is based on the Subtraction Property of Equality, while the second match is based on Substitution.

Step-by-step explanation:

In the given proof, we have two statements:

m∠1 + m∠5 = 180° and m∠1 + m∠4 = 180°

m∠1 + m∠5 = m∠1 + m∠4

To match the reasons to these statements, we can use the following:

Subtraction Property of Equality - This property states that if a=b, then a-c=b-c. In this case, subtracting m∠1 from both sides of the equation gives m∠1 + m∠5 - m∠1 = m∠1 + m∠4 - m∠1, which simplifies to m∠5 = m∠4.

Substitution - This is a basic algebraic technique where we can substitute one expression with another equal expression. In this case, we can substitute m∠1 + m∠5 with m∠1 + m∠4.

Therefore, the correct matches are:

m∠1 + m∠5 = 180° and m∠1 + m∠4 = 180° - Subtraction Property of Equality

m∠1 + m∠5 = m∠1 + m∠4 - Substitution

Answer 2

Step-by-step explanation:

Let set up the two column proof

Statements. Reasons

1. m 1+ m∠5 = 180° and m∠1 + m∠4=180° Given

2. 2. m∠1 + m∠5 = m∠1 + m∠4. Substitution

3.m∠5 = m∠4. Subtraction Property of Equal

4.is Parallel to Given. 4.If alternate interior angles equal, then lines are ||.