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)
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

Answer 1

To fill in the two-column proof that parallelogram ABCD with congruent diagonals DB and AC is a rectangle, we need to arrange the statements and reasons in a logical sequence. Here's how you can organize them:

Proof

| 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 (same angles from congruent triangles) | | 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 (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 |

Make sure to place the correct statements and reasons in the appropriate places; this sequence illustrates how to conclude that the given parallelogram is a rectangle based on the properties of congruent angles and sides.