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°

2. m∠1 + m∠5 = m∠1 + m∠4

3. m∠5 = m∠4

4. Ray YZ is parallel to Ray UV

Given
Substitution
Subtraction property of equality
If alternate interior angles equal, then line are ||

Answer 1

Answer and Step-by-step explanation:

Since we have given that

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

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

3. m∠5 = m∠4 -

Subtraction property of equality

4. Ray YZ is parallel to Ray UV - If alternate interior angles equal, then line are ||

Answer 2

Mathematical proofs are used to prove equal segments, equal angles, parallel segments, and several others.

The statements and the reasons for the proof are:

1. $\mathbf{\angle 1 + \angle 5 = 180^o}$    $\mathbf{\angle 1 + \angle 4 = 180^o}$ ------- Given
2. $\mathbf{\angle 1 + \angle 5 = \mathbf{\angle 1 + \angle 4 }}$ ---- Substitution
3. $\mathbf{\angle 5 = \angle 4 }$ ------ Subtraction property of equality
4. Ray YZ is parallel to Ray UV ------- If alternate interior angles equal, then line are ||

The given parameters are:

$\mathbf{\angle 1 + \angle 5 = 180^o}$ and $\mathbf{\angle 1 + \angle 4 = 180^o}$

So, the first statement would be:

$\mathbf{\angle 1 + \angle 5 = 180^o}$

$\mathbf{\angle 1 + \angle 4 = 180^o}$

Reason: Given

Next, we substitute $\mathbf{\angle 1 + \angle 4 }$ for $\mathbf{180^o}$ in $\mathbf{\angle 1 + \angle 5 = 180^o}$

So, we have:

$\mathbf{\angle 1 + \angle 5 = \mathbf{\angle 1 + \angle 4 }}$

This means that, the second statement would be

$\mathbf{\angle 1 + \angle 5 = \mathbf{\angle 1 + \angle 4 }}$

Reason: Substitution

Subtract $\mathbf{\angle 1 }$ from both sides.

So, we have:

$\mathbf{\angle 5 = \angle 4 }$

This means that, the third statement would be

$\mathbf{\angle 5 = \angle 4 }$

Reason: Subtraction property of equality

The previous statement implies that; alternate angles are equal.

So, the fourth statement would be:

Ray YZ is parallel to Ray UV

Reason: If alternate interior angles equal, then line are ||

Read more about mathematical proofs at:

https://brainly.com/question/2010495