Question

Match the reasons to the statements in the proof.

Answer 1

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 lines are ||. 

Answer 2

Answer:

1. $m\angle 1+m\angle 5=180^{\circ}$ and $m\angle 1+m\angle 4=180^{\circ}$; given

2. $m\angle 1+m\angle5=m\angle 1+m\angle4$; substitution

3.$m\angle5=m\angle4$; subtraction property of equality

4. Ray YZ is parallel to ray UV; if alternate interior angles equal , then lines are parallel.

Step-by-step explanation:

Given

$m\angle1+m\angle5=180^{\circ}$

$m\angle 1+m\angle4=180^{\circ}$

To prove that YZ is parallel to UV.

Proof:

1.Statement: $m\angle 1+m\angle5=180^{\circ}$ and $m\angle1+m\angle4=180^{\circ}$

Reason; Given

2. Statement: $m\angle1+m\angle5=m\angle 1+m\angle4$

Reason: By using substitution property

3.Statement: $m\angle5=m\angle4$

Reason: Subtraction property of equality.

4.Statement: Ray YZ is parallel to Ray UV

Reason: If alternate interior angles equal, then lines are parallel.