Question

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

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

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.

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.