Alternate interior angles are formed on the opposite sides of the line of transversal and inside the two lines. The line of transversal passes through the two lines who are coplanar at distinct points. The alternate interior angles will be on the opposite sides to this line and will always be inside the line. These angles can tell whether the two lines are parallel to each other or not. If these angles are equal then the two lines are parallel.
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The angles which are on the opposite sides of the line of transversal and
created between the two coplanar lines are known as alternate interior angles.
The alternate interior angles will be congruent if the transversal will cut through a set of parallel lines.
Given: The parallel lines are "l" and "m" and line 't' is the transversal.
Proof:
Statement 
Reasons 

Step 1:  $l$ and $m$ are parallel lines and $t$ is the transversal. 
Given 
Step 2:  $\angle$ 2 and $\angle$ 6 are congruent ($\angle$ 2 = $\angle$ 6)  Corresponding angles 
Step 3:  $\angle$ 4 and $\angle$ 6 are congruent ($\angle$ 4 = $\angle$ 6)  Vertically opposite angles 
Step 4:  $\angle$ 4 and $\angle$ 6 are congurent ($\angle$ 4 = $\angle$ 6)  From Step 2 and Step 3 (Using transitive property). 
Find the value of angle a and b in the figure given below.
As 76° and b are alternate interior angles, they are congruent.
So, b = 76°
As 104° and a are alternate interior angles, they are congruent.
So, a = 104°
Find the missing angles x , y and z in the following figure.
As the pair 98°, x and z, y are alternate interior angles, they are equal in measure.
So, x = 98°
98° + y = 180°
y = 180°  98°
= 82°
Since z and y are alternate interior angles, they are equal in measure
So, z = 82°
More topics in Alternate Interior Angles  
Alternate Interior Angles Theorem  
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