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

Question

substitution property of equality
transitive property of congruence
m<bad/2=90
CPCTC theorem of congruence
M<BAD=90

Answer 1

Here’s how to correctly organize the statements and reasons for the proof that parallelogram ABCD with congruent diagonals is a rectangle:

Statements and Reasons

| 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 | CPCTC (Corresponding Parts of Congruent Triangles are Congruent) | | 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° | Substitute m∠ABC for m∠BAD (substitution property of equality) | | 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 organization reflects the logical progression from assumptions (like the properties of parallelograms) to the conclusions necessary to show that ABCD is a rectangle.