Question

He makes the following table to prove that the alternate interior angles are equal:

Statement Justification
angle 2 = angle 6 ?
angle 2 = angle 4 Vertical angles are congruent.
angle 4 = angle 6 transitive property of equality.
angle 2 = angle 6,
angle 2 = angle 4,
therefore angle 4 = angle 6
Which is the missing justification?
a. Co-exterior angles formed by a transversal on parallel lines are congruent.
b. Corresponding angles formed by a transversal on parallel lines are congruent.
c. Co-interior angles formed by a transversal on parallel lines are congruent.
d. Corresponding angles formed by a transversal on parallel lines are supplementary.

Answer 1

The missing justification in the table is that corresponding angles formed by a transversal on parallel lines are supplementary.

Step-by-step explanation:

The missing justification is d. Corresponding angles formed by a transversal on parallel lines are supplementary.

In the given table, angle 2 and angle 6 are alternate interior angles, which are equal because the vertical angles formed by angle 2 are congruent. Similarly, angle 4 and angle 6 are equal because they are vertical angles. Therefore, angle 4 is equal to angle 6. This justifies the statement that angle 2 is equal to angle 6.