Use the image to answer the question.

Question

Two parallel horizontal lines a and b, intersecting with two parallel slanted lines e and f. A parallelogram is formed in the center of the intersecting lines.

In the diagram, a∥b
and e∥f
. Sylvia writes a proof to prove that opposite angles, ∠6
and ∠11
, are congruent in the parallelogram. Drag and drop the statements and reasons into their correct locations in the two-column proof.

(2 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Statement Reason
1. a∥b
and e∥f
given
2. Response area Corresponding Angles Theorem
3. m∠5+m∠6=180°
and m∠9+m∠11=180°
definition of linear pair
4. m∠13+m∠6=180°
and m∠13+m∠11=180°
Response area
5. Response area Transitive Property of Equality
6. m∠6=m∠11
Response area

The option "CPCTC Theorem" (6 of 6) has been selected. Press tab to choose a response area, and spacebar to insert it. Press escape to cancel.

Answer 1

Here is the correct configuration of the two-column proof with the statements and reasons appropriately matched:

| Statement | Reason | |---------------------------------------------------|----------------------------------------------| | 1. a∥b and e∥f | Given | | 3. m∠5 + m∠6 = 180° and m∠9 + m∠11 = 180° | Definition of linear pair | | 4. m∠13 + m∠6 = 180° and m∠13 + m∠11 = 180° | Linear pair (angles on the same line) | | 2. m∠6 = m∠11 | Corresponding Angles Theorem | | 5. m∠6 = m∠11 | Transitive Property of Equality | | 6. m∠6 = m∠11 | CPCTC Theorem |

To summarize:

• Statement 2 fits after statement 4 because corresponding angles are equal when parallel lines are cut by a transversal.
• Statement 5 should come directly after the conclusion of angle measures from other known equalities, making use of the Transitive Property.
• Finally, we restate the conclusion with CPCTC (Corresponding Parts of Congruent Triangles are Congruent) to show that the angles from the triangles are indeed equal.

Make sure to adjust the placement of these in your proof according to this logical flow.