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Match the reasons to the statements in the proof.

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. Ray YZ is parallel to Ray UV
Given

Match the reasons to the statements in the proof 1 m1 m5 180 and m1 m4180 Subtraction property of equality 2 m1 m5 m1 m4 Substitution 3 m5 m4 If alternate inter class=

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choixongdong
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 ||. 
lublana

Answer:

1. [tex]m\angle 1+m\angle 5=180^{\circ}[/tex] and [tex]m\angle 1+m\angle 4=180^{\circ}[/tex]; given

2. [tex]m\angle 1+m\angle5=m\angle 1+m\angle4[/tex]; substitution

3.[tex]m\angle5=m\angle4[/tex]; 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

[tex]m\angle1+m\angle5=180^{\circ}[/tex]

[tex]m\angle 1+m\angle4=180^{\circ}[/tex]

To prove that YZ is parallel to UV.

Proof:

1.Statement: [tex]m\angle 1+m\angle5=180^{\circ}[/tex] and [tex]m\angle1+m\angle4=180^{\circ}[/tex]

Reason; Given

2. Statement: [tex]m\angle1+m\angle5=m\angle 1+m\angle4[/tex]

Reason: By using substitution property

3.Statement: [tex]m\angle5=m\angle4[/tex]

Reason: Subtraction property of equality.

4.Statement: Ray YZ is parallel to Ray UV

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

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