Use the image to answer the question.

Question

A quadrilateral upper A upper B upper C upper D. Two diagonals connect opposing vertices upper A to upper C and upper B to upper D. The point of intersection is upper O.

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)
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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

Answer 1

Here is the two-column proof that parallelogram ABCD with congruent diagonals DB and AC is a rectangle. I will place the statements in order with their appropriate reasons:

| 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. ΔBAD ≅ ΔABC | SSS Congruence Theorem | | 6. ∠BAD ≅ ∠ABC | 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° | Substituting m∠ABC for 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 correctly aligns the statements and reasons in accordance with the proof structure for demonstrating that parallelogram ABCD is a rectangle due to having congruent diagonals and right angles.