Rectangle Proofs Quick Check5 of 5 5 of 5 ItemsQuestionUse the image to answer the question.Drag and drop the statements and reasons into their correct locations in the two-column proof that parallelogram ABCD with congruent diagonals DB¯¯¯¯¯¯¯¯ and AC¯¯¯¯¯¯¯¯ is a rectangle.(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 Reason1. ABCD is a parallelogram. Given2. DB¯¯¯¯¯¯¯¯≅AC¯¯¯¯¯¯¯¯ Given3. DA¯¯¯¯¯¯¯¯≅CB¯¯¯¯¯¯¯¯ Opposite sides of a parallelogram are congruent.4. AB¯¯¯¯¯¯¯¯≅BA¯¯¯¯¯¯¯¯ Reflexive Property of Congruence5. △BAD≅△ABC SSS Congruence Theorem6. ∠BAD≅∠ABC Response area7. m∠BAD=m∠ABC Definition of congruence8. m∠BAD+m∠ABC=180° Consecutive angles of a parallelogram are supplementary9. m∠BAD+m∠BAD=180° Response area10. 2m∠BAD=180° Combine like terms11. Response area Division Property of Equality12. m∠ABC=90° Transitive Property of Equality13. m∠ADC=m∠DAB=90° Opposite angles of a parallelogram are congruent14. ∠BAD, ∠DCB, ∠ABC, and ∠ADC are right angles Definition of a right angle15. ABCD is a rectangle Definition of a rectangleTransitive Property of Congruencem∠BAD=90°m∠BAD2=90°CPCTC Theorem of CongruenceSubstitution Property of Equality

Question

Rectangle Proofs Quick Check5 of 5 5 of 5 ItemsQuestionUse the image to answer the question.Drag and drop the statements and reasons into their correct locations in the two-column proof that parallelogram ABCD with congruent diagonals DB¯¯¯¯¯¯¯¯ and AC¯¯¯¯¯¯¯¯ is a rectangle.(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 Reason1. ABCD is a parallelogram. Given2. DB¯¯¯¯¯¯¯¯≅AC¯¯¯¯¯¯¯¯ Given3. DA¯¯¯¯¯¯¯¯≅CB¯¯¯¯¯¯¯¯ Opposite sides of a parallelogram are congruent.4. AB¯¯¯¯¯¯¯¯≅BA¯¯¯¯¯¯¯¯ Reflexive Property of Congruence5. △BAD≅△ABC SSS Congruence Theorem6. ∠BAD≅∠ABC Response area7. m∠BAD=m∠ABC Definition of congruence8. m∠BAD+m∠ABC=180° Consecutive angles of a parallelogram are supplementary9. m∠BAD+m∠BAD=180° Response area10. 2m∠BAD=180° Combine like terms11. Response area Division Property of Equality12. m∠ABC=90° Transitive Property of Equality13. m∠ADC=m∠DAB=90° Opposite angles of a parallelogram are congruent14. ∠BAD, ∠DCB, ∠ABC,  and ∠ADC are right angles Definition of a right angle15. ABCD is a rectangle Definition of a rectangleTransitive Property of Congruencem∠BAD=90°m∠BAD2=90°CPCTC Theorem of CongruenceSubstitution Property of Equality

GPT-4o mini · Answer

To set up the two-column proof that parallelogram \(ABCD\) with congruent diagonals \(DB\) and \(AC\) is a rectangle, you can organize the statements and reasons as follows:

| Statements | Reasons | |------------|---------| | 1. \(ABCD\) is a parallelogram. | Given | | 2. \(DB \cong AC\) | Given | | 3. \(DA \cong CB\) | Opposite sides of a parallelogram are congruent. | | 4. \(AB \cong BA\) | Reflexive Property of Congruence | | 5. \(\triangle BAD \cong \triangle ABC\) | SSS Congruence Theorem | | 6. \(\angle BAD \cong \angle ABC\) | CPCTC | | 7. \(m\angle BAD = m\angle ABC\) | Definition of congruence | | 8. \(m\angle BAD + m\angle ABC = 180^\circ\) | Consecutive angles of a parallelogram are supplementary. | | 9. \(m\angle BAD + m\angle BAD = 180^\circ\) | Substitution | | 10. \(2m\angle BAD = 180^\circ\) | Combine like terms | | 11. \(m\angle BAD = 90^\circ\) | Division Property of Equality | | 12. \(m\angle ABC = 90^\circ\) | Transitive Property of Equality | | 13. \(m\angle ADC = m\angle DAB = 90^\circ\) | Opposite angles of a parallelogram are congruent. | | 14. \(\angle BAD, \angle DCB, \angle ABC, \text{ and } \angle ADC\) are right angles | Definition of a right angle | | 15. \(ABCD\) is a rectangle | Definition of a rectangle |

Please fill in response areas where specific statements or reasons were indicated, using the provided responses. The layout should guide you to ascertain the correct sequence in forming the two-column proof.