Question
The quadrilateral A B C D is a parallelogram with diagonals that cross at E.
Quadrilateral A B C D.Short description, Quadrilateral A B C D.,Long description,
Quadrilateral A B C D has diagonals A C and B D drawn, dividing the parallelogram into 4 triangles that meet at point E. The base of triangle A B E is opposite the base of triangle C D E.
Question
Move the options to the spaces to complete the proof that triangle A B E is congruent to triangle C D E.
Response area with 4 blank spaces
Because A B C D is a parallelogram, we know that the
Blank space 1 empty
. Thus,
Blank space 2 empty
and
Blank space 5 empty
.
From the definition of a parallelogram, we know that the opposite sides are congruent. Therefore,
Blank space 7 empty
.
By side-side-side congruency, this shows that triangle A B E is congruent to triangle C D E.
Answer options with 10 options.
Quadrilateral A B C D.Short description, Quadrilateral A B C D.,Long description,
Quadrilateral A B C D has diagonals A C and B D drawn, dividing the parallelogram into 4 triangles that meet at point E. The base of triangle A B E is opposite the base of triangle C D E.
Question
Move the options to the spaces to complete the proof that triangle A B E is congruent to triangle C D E.
Response area with 4 blank spaces
Because A B C D is a parallelogram, we know that the
Blank space 1 empty
. Thus,
Blank space 2 empty
and
Blank space 5 empty
.
From the definition of a parallelogram, we know that the opposite sides are congruent. Therefore,
Blank space 7 empty
.
By side-side-side congruency, this shows that triangle A B E is congruent to triangle C D E.
Answer options with 10 options.
Answers
GPT-4o mini
To complete the proof that triangle ABE is congruent to triangle CDE, we can use the properties of parallelograms and the Side-Side-Side (SSS) congruence postulate.
Here is a suggested way to fill in the blanks:
**Response area with 4 blank spaces:**
Because A B C D is a parallelogram, we know that the
**Blank space 1**: opposite sides are congruent. Thus,
**Blank space 2**: A B ≅ C D
and
**Blank space 3**: A E ≅ C E.
From the definition of a parallelogram, we know that the opposite sides are congruent. Therefore,
**Blank space 4**: B D ≅ A C.
By side-side-side congruency, this shows that triangle A B E is congruent to triangle C D E.
**Answer options you can use to fill in the blanks:**
1. opposite sides are congruent.
2. A B ≅ C D
3. A E ≅ C E
4. B D ≅ A C
5. triangles ABE and CDE
6. the diagonals bisect each other
7. triangle ABE ≅ triangle CDE
8. angle ABE ≅ angle CDE
9. angle ABE and angle CDE are corresponding angles
10. the segments AE and CE are equal
Feel free to adjust the placement of the answer options to ensure clarity and correct logical flow in your argument!
Here is a suggested way to fill in the blanks:
**Response area with 4 blank spaces:**
Because A B C D is a parallelogram, we know that the
**Blank space 1**: opposite sides are congruent. Thus,
**Blank space 2**: A B ≅ C D
and
**Blank space 3**: A E ≅ C E.
From the definition of a parallelogram, we know that the opposite sides are congruent. Therefore,
**Blank space 4**: B D ≅ A C.
By side-side-side congruency, this shows that triangle A B E is congruent to triangle C D E.
**Answer options you can use to fill in the blanks:**
1. opposite sides are congruent.
2. A B ≅ C D
3. A E ≅ C E
4. B D ≅ A C
5. triangles ABE and CDE
6. the diagonals bisect each other
7. triangle ABE ≅ triangle CDE
8. angle ABE ≅ angle CDE
9. angle ABE and angle CDE are corresponding angles
10. the segments AE and CE are equal
Feel free to adjust the placement of the answer options to ensure clarity and correct logical flow in your argument!