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 response input area to answer the question. Select a response, navigate to the desired input area 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
Two-Column Proof
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
Press enter key to drop response here.the reason that justifies the statement angle upper B upper A upper D is congruent to angle upper A upper B upper C
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°
Press enter key to drop response here.the reason that justifies the statement the measure of angle upper B upper A upper D plus the measure of angle upper B upper A upper D equals 180 degrees
10. 2m∠BAD=180°
Combine like terms.
11. Press enter key to drop response here.the statement that aligns to the Division Property of Equality 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

Fill-ins:

6. Reason: Corresponding parts of congruent triangles are congruent (CPCTC).

9. Reason: Substitution Property of Equality.

11. Statement: m∠BAD = 90° (with reason: Division Property of Equality).

These complete the proof that ABCD is a rectangle.