Question

Match the reasons with the statements in the proof.

Answer 1

Answer:

Given: $m\angle 1 = m\angle 3$ and $m\angle 2 = m\angle 3$

To prove that:

$l || m$

1. $m\angle 1 = m\angle 3$          [Given]

$m\angle 2 = m\angle 3$

Substitution property of equality says that:

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

2 $m\angle 1 = m\angle 2$          [ 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. $\angle 1$ and  $\angle 2$ 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. $l || m$ ; then the lines are parallel     [By Alternate interior angles theorem]

Correct match is as follows:

1. $m\angle 1 = m\angle 3$          [Given]

 $m\angle 2 = m\angle 3$

2. $m\angle 1 = m\angle 2$          [Substitution]

3. $\angle 1$ and  $\angle 2$ are alternate interior angle       [By definition of alternate interior angles ]

4. $l || m$ the lines are parallel  [If alternate interior angles are equal]

Answer 2

Observe the given figure.

Given: $m \angle 1 = m \angle 3, m \angle 2 = m \angle 3$

To prove: $l \parallel m$

Statement                                                      

1.  $m \angle 1 = m \angle 3, m \angle 2 = m \angle 3$

Reason: Given

2. $m \angle 1 = m \angle 2$

Reason: Substitution

3. $\angle 1,\angle 2$ are alternate interior angles.

Reason: Definition of alternate interior angles

4. $l \parallel m$

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