Given: Lines p and q are parallel and r is a transversal. Prove: ∠2 ≅ ∠7

Parallel lines p and q are cut by transversal r. On line p where it intersects with line r, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are: 1, 2, 4, 3. On line q where it intersects with line r, 4 angles are created. Labeled clockwise, from the uppercase left, the angles are: 5, 6, 8, 7.
A 2-column table with 4 rows. Column 1 is labeled statements with the entries p is parallel to q and r is a transversal, A, B, angle 2 is congruent to angle 7. Column 2 is labeled reasons with the entries given, vertical angles are congruent, correlated angle theorem, transitive property.

Which statements could complete the proof?

The statement A is Angle 2 is congruent to angle 3

The statement is Angle 3 is congruent to angle 7

Step-by-step explanation:

The given information are;

The given parallel lines = p and q

The given transversal = r

The angles from the top left at the intersection of p and r = 1, 2, 4, 3

The angles from the top left at the intersection of q and r = 5, 6, 8, 7

The 2-column table is presented as follows;

Statement                                                          Reasons

p is parallel to q and r is a transversal             Given

A                                                                          Vertical angles are congruent

B                                                                          Correlated angle theorem

Angle 2 is congruent to angle 7                        Transitive property

We have the orientation of the angles given as follows;

1, 2

3, 4

5, 6

7, 8

Therefore, we have;

A = Angle 2 is congruent to angle 3   Vertical angles are congruent

B = Angle 3 is congruent to angle 7     Correlated angle theorem

To give;

Statement                                                          Reasons

p is parallel to q and r is a transversal             Given

Angle 2 is congruent to angle 3                       Vertical angles are congruent

Angle 3 is congruent to angle 7                       Correlated angle theorem

Angle 2 is congruent to angle 7                       Transitive property

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step-by-step explanation: