Using alternate interior angles to show two lines are parallel

The video tutorial explains how to determine if two lines, M and N, are parallel by using the concept of alternate interior angles. It introduces the theorem of alternate interior angles, which states that if these angles are equal, the lines are parallel. The tutorial demonstrates setting the angles equal to each other and solving for the variable X to prove their equality. When X equals 63, the angles are equal, confirming that lines M and N are parallel.

What is the relationship between alternate interior angles and parallel lines?

• They are equal when the lines are perpendicular.

• They are never equal.

• They are equal when the lines are parallel.

• They are always equal.

What is the first step in proving that two angles are equal?

• Subtract the angles.

• Add the angles.

• Set the angles equal to each other.

• Multiply the angles.

What equation is set up to solve for X in the proof?

• 21 - X = 84

• 21 + X = 84

• X + 21 = 84

• X - 21 = 84

What is the value of X that makes the angles equal?

• 63

• 42

• 21

• 84

What conclusion can be drawn when the alternate interior angles are equal?

• The lines are perpendicular.

• The lines are skew.

• The lines are parallel.

• The lines are intersecting.