A conjecture and the paragraph proof used to prove the conjecture are shown. Given: R S T U is a parallelogram. Angle 1 and angle 3 are complementary. Prove: angle 2 and angle 3 are complementary. Angle R U S is labeled 1. Angle U S T is labeled 2. A ray is extended diagonally up to the left of UT forming an interior angle labeled as 3. Drag an expression or phrase to each box to complete the proof. 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. It is given that RSTU is a parallelogram, so RU¯¯¯¯¯∥ST¯¯¯¯¯ by the definition of parallelogram. Therefore, ∠1≅∠2 ​by the alternate interior angles theorem, and m∠1=m∠2 ​by the Response area. It is also given that ∠1 and ∠3 are complementary, so m∠1+m∠3=90° by the Response area. By substitution, m∠2+ Response area = 90°, and so ∠2 and Response area are complementary by the definition of complementary.