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=190°
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
Statement Reason
1. ABCD Given
is a parallelogram.
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.
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=190°
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 Definition of a right angle
are right angles
15. ABCD Definition of a rectangle