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 Reason 1. ABCD is a parallelogram. Given 2. DB¯¯¯¯¯¯¯¯≅AC¯¯¯¯¯¯¯¯ Given 3. DA¯¯¯¯¯¯¯¯≅CB¯¯¯¯¯¯¯¯ Opposite sides of a parallelogram are congruent. 4. AB¯¯¯¯¯¯¯¯≅BA¯¯¯¯¯¯¯¯ Reflexive Property of Congruence 5. △BAD≅△ABC SSS Congruence Theorem 6. ∠BAD≅∠ABC Response area 7. m∠BAD=m∠ABC Definition of congruence 8. m∠BAD+m∠ABC=180° Consecutive angles of a parallelogram are supplementary 9. m∠BAD+m∠BAD=180° Response area 10. 2m∠BAD=180° Combine like terms 11. Response area Division Property of Equality 12. m∠ABC=90° Transitive Property of Equality 13. m∠ADC=m∠DAB=90° Opposite angles of a parallelogram are congruent 14. ∠BAD , ∠DCB , ∠ABC , and ∠ADC are right angles Definition of a right angle 15. ABCD is a rectangle Definition of a rectangle Skip to navigation

Answer 1

Here’s how to organize the statements and reasons into a two-column proof that parallelogram ABCD is a rectangle:

Statements | Reasons --- | ---

1. ABCD is a parallelogram. | Given
2. DB≅AC | Given
3. DA≅CB | Opposite sides of a parallelogram are congruent.
4. AB≅BA | Reflexive Property of Congruence
5. △BAD≅△ABC | SSS Congruence Theorem
6. ∠BAD≅∠ABC | Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
7. m∠BAD = m∠ABC | Definition of congruence
8. m∠BAD + m∠ABC = 180° | Consecutive angles of a parallelogram are supplementary
9. m∠BAD + m∠BAD = 180° | Substitution (replacing m∠ABC with m∠BAD)
10. 2m∠BAD = 180° | Combine like terms
11. m∠BAD = 90° | Division Property of Equality
12. m∠ABC = 90° | Transitive Property of Equality
13. m∠ADC = m∠DAB = 90° | Opposite angles of a parallelogram are congruent
14. ∠BAD, ∠DCB, ∠ABC, and ∠ADC are right angles | Definition of a right angle
15. ABCD is a rectangle. | Definition of a rectangle

This arrangement uses the given information to show that ABCD has all the properties of a rectangle, particularly that all angles are right angles due to the congruence of the diagonals.