Match the reasons with the statements in the proof. given: j | | k m 1 = m 3 prove: l | | m 1. j||k, m? 3 = m? 1 given 2. m? 1 = m? 2 if alternate interior angles are =, then lines are ||. 3. m? 2 = m? 3 if lines are ||, then corresponding angles are =. 4. l||m substitution

please see image attached. Let me know if you have questions.

please see image attached. Let me know if you have questions.

Step-by-step explanation:

Given: c is parallel to d and ∠4=∠5.

To prove: ∠7=∠8

Proof:

Statement                                                Reason

1. c║d, ∠4=∠5                                           Given

2.∠4=∠7                                    If lines ||, alternate interior angles are equal.

3.∠5=∠8                                             Vertical angles are equal

Since, ∠4=∠5, therefore ∠7=∠8

4.∠7=∠8                                               Substitution

By the corresponding angle theorem : The corresponding angles made by a same transversal on two parallel lines are equal in measure.

By the converse of alternate angles : When alternative angles in two lines by same transversal are equal then these lines are parallel to each other,

Now, given,

j ║ k

m∠1 = m∠3

Prove:  l ║ m,

Thus, the column proof would be,

    Statement                       Reason

1. j ║k, m∠1 = m∠3            Given

2. m∠1 = m∠2                    If lines are ║, then corresponding angles are =

3. m∠2 = m∠3                   Substitution

4.  l ║ m                             If alternative angles are =, then lines are ║

Given: and

To prove that:

1.          [Given]

Substitution property of equality says that:

If x = y, then x can be substituted in y, or y can be substituted in x.

2          [ By Substitution Property]

Alternate interior angles states that when two lines are crossed by transversal , a pair of angles on the inner sides of each of these two lines on the opposite sides of the transversal line.

3. and   are alternate interior angles  [By definition Alternate interior angle].

Alternating interior angles theorem states that if two parallel lines are intersected by third lines, then the angles in the inner sides of the parallel lines on the opposite sides of the transversal are equal.

4. ; then the lines are parallel     [By Alternate interior angles theorem]

Correct match is as follows:

1.          [Given]

2.          [Substitution]

3. and   are alternate interior angle       [By definition of alternate interior angles ]

4. the lines are parallel  [If alternate interior angles are equal]

Given: and

To prove that:

1.          [Given]

Substitution property of equality says that:

If x = y, then x can be substituted in y, or y can be substituted in x.

2          [ By Substitution Property]

Alternate interior angles states that when two lines are crossed by transversal , a pair of angles on the inner sides of each of these two lines on the opposite sides of the transversal line.

3. and   are alternate interior angles  [By definition Alternate interior angle].

Alternating interior angles theorem states that if two parallel lines are intersected by third lines, then the angles in the inner sides of the parallel lines on the opposite sides of the transversal are equal.

4. ; then the lines are parallel     [By Alternate interior angles theorem]

Correct match is as follows:

1.          [Given]

2.          [Substitution]

3. and   are alternate interior angle       [By definition of alternate interior angles ]

4. the lines are parallel  [If alternate interior angles are equal]

Observe the given figure.

Given:

To prove:

Statement                                                      

1.  

Reason: Given

2.

Reason: Substitution

3. are alternate interior angles.

Reason: Definition of alternate interior angles

4.

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

Observe the given figure.

Given:

To prove:

Statement                                                      

1.  

Reason: Given

2.

Reason: Substitution

3. are alternate interior angles.

Reason: Definition of alternate interior angles

4.

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

Please find the attachment.

We have been given that and b||c.

Let us match the reasons with given statements in the proof.

Since we know that if two lines are parallel then corresponding angles will be equal. So by corresponding angles .

By substitution we will get,

Therefore,

Since we know that if the alternate interior angles are equal, then lines are parallel.

Hence proved that a||b.  

Please find the attachment.

We have been given that and b||c.

Let us match the reasons with given statements in the proof.

Since we know that if two lines are parallel then corresponding angles will be equal. So by corresponding angles .

By substitution we will get,

Therefore,

Since we know that if the alternate interior angles are equal, then lines are parallel.

Hence proved that a||b.