Question
Given: Quadrilateral A B C D with segment A D is congruent to segment B C, segment A B is congruent to segment D C
Prove: A B C D is a parallelogram
Quadrilateral A B C D shows diagonal A C.
Question
Move statements and reasons to the table to complete the proof.
Response area with 5 blank spaces
Statements Reasons
Quadrilateral A B C D with segment A D is congruent to segment B C, segment A B is congruent to segment D C Given
Blank space 1 empty
Reflexive Property
Blank space 2 empty
Blank space 3 empty
angle D A C is congruent to angle B C A, angle D C A is congruent to angle B A C
Blank space 4 empty
Blank space 5 empty
Converse of Alternate Interior Angles Theorem
A B C D is a parallelogram Definition of parallelogram
Answer options with 9 options.
Prove: A B C D is a parallelogram
Quadrilateral A B C D shows diagonal A C.
Question
Move statements and reasons to the table to complete the proof.
Response area with 5 blank spaces
Statements Reasons
Quadrilateral A B C D with segment A D is congruent to segment B C, segment A B is congruent to segment D C Given
Blank space 1 empty
Reflexive Property
Blank space 2 empty
Blank space 3 empty
angle D A C is congruent to angle B C A, angle D C A is congruent to angle B A C
Blank space 4 empty
Blank space 5 empty
Converse of Alternate Interior Angles Theorem
A B C D is a parallelogram Definition of parallelogram
Answer options with 9 options.
Answers
GPT-4o mini
To complete the proof that quadrilateral ABCD is a parallelogram, we can fill in the blank spaces as follows:
| Statements | Reasons |
|------------|---------|
| Quadrilateral A B C D with segment A D is congruent to segment B C, segment A B is congruent to segment D C. | Given |
| **Blank space 1:** angle D A C is congruent to angle B C A | **Reason:** Alternate Interior Angles Theorem |
| **Blank space 2:** angle D A C + angle D C A = 180 degrees | **Reason:** Linear Pair (if lines intersect, adjacent angles are supplementary) |
| **Blank space 3:** angle B C A + angle A B D = 180 degrees | **Reason:** Linear Pair (if lines intersect, adjacent angles are supplementary) |
| angle D A C is congruent to angle B C A, angle D C A is congruent to angle B A C | **Reason:** Given (from previous congruences) |
| **Blank space 4:** angle A D C is congruent to angle B C A | **Reason:** Corresponding Angles Postulate |
| **Blank space 5:** A B C D is a parallelogram | **Reason:** Definition of parallelogram |
With these completed blanks, the proof is structured to show that because pairs of alternate interior angles are congruent and both pairs of opposite sides are congruent, ABCD must be a parallelogram.
| Statements | Reasons |
|------------|---------|
| Quadrilateral A B C D with segment A D is congruent to segment B C, segment A B is congruent to segment D C. | Given |
| **Blank space 1:** angle D A C is congruent to angle B C A | **Reason:** Alternate Interior Angles Theorem |
| **Blank space 2:** angle D A C + angle D C A = 180 degrees | **Reason:** Linear Pair (if lines intersect, adjacent angles are supplementary) |
| **Blank space 3:** angle B C A + angle A B D = 180 degrees | **Reason:** Linear Pair (if lines intersect, adjacent angles are supplementary) |
| angle D A C is congruent to angle B C A, angle D C A is congruent to angle B A C | **Reason:** Given (from previous congruences) |
| **Blank space 4:** angle A D C is congruent to angle B C A | **Reason:** Corresponding Angles Postulate |
| **Blank space 5:** A B C D is a parallelogram | **Reason:** Definition of parallelogram |
With these completed blanks, the proof is structured to show that because pairs of alternate interior angles are congruent and both pairs of opposite sides are congruent, ABCD must be a parallelogram.