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Is quadrilateral ABCD a parallelogram?
(1) All four internal angles of ABCD are equal.
(2) AC, a diagonal of ABCD, divides ABCD into two congruent triangles.
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
  • c)
    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
  • d)
    EACH statement ALONE is sufficient to answer the question asked
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Is quadrilateral ABCD a parallelogram?(1) All four internal angles of ...
Statement 1: All four internal angles of ABCD are equal.
If all four internal angles of ABCD are equal, it implies that opposite angles are congruent. In a parallelogram, opposite angles are always congruent. Therefore, statement 1 alone is sufficient to determine that quadrilateral ABCD is a parallelogram.
Statement 2: AC, a diagonal of ABCD, divides ABCD into two congruent triangles.
If AC, a diagonal of ABCD, divides ABCD into two congruent triangles, it suggests that opposite sides and opposite angles are congruent. However, this information alone does not guarantee that the opposite sides are parallel, which is a defining characteristic of a parallelogram. Therefore, statement 2 alone is not sufficient to determine if quadrilateral ABCD is a parallelogram.
By considering both statements together, we have information about the equality of internal angles and the division of the quadrilateral into congruent triangles. This combination of information implies that opposite angles and sides are congruent, which is a defining property of a parallelogram. Therefore, both statements together are sufficient to determine that quadrilateral ABCD is a parallelogram.
As a result, the correct answer is A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
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Most Upvoted Answer
Is quadrilateral ABCD a parallelogram?(1) All four internal angles of ...
Statement 1: All four internal angles of ABCD are equal.
If all four internal angles of ABCD are equal, it implies that opposite angles are congruent. In a parallelogram, opposite angles are always congruent. Therefore, statement 1 alone is sufficient to determine that quadrilateral ABCD is a parallelogram.
Statement 2: AC, a diagonal of ABCD, divides ABCD into two congruent triangles.
If AC, a diagonal of ABCD, divides ABCD into two congruent triangles, it suggests that opposite sides and opposite angles are congruent. However, this information alone does not guarantee that the opposite sides are parallel, which is a defining characteristic of a parallelogram. Therefore, statement 2 alone is not sufficient to determine if quadrilateral ABCD is a parallelogram.
By considering both statements together, we have information about the equality of internal angles and the division of the quadrilateral into congruent triangles. This combination of information implies that opposite angles and sides are congruent, which is a defining property of a parallelogram. Therefore, both statements together are sufficient to determine that quadrilateral ABCD is a parallelogram.
As a result, the correct answer is A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
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Is quadrilateral ABCD a parallelogram?(1) All four internal angles of ...

Statement Analysis:

Statement 1: All four internal angles of quadrilateral ABCD are equal.
Statement 2: AC, a diagonal of ABCD, divides ABCD into two congruent triangles.

Analysis:

Statement 1 alone: If all four internal angles of a quadrilateral are equal, it implies that the quadrilateral is a parallelogram. Therefore, statement 1 alone is sufficient to answer the question.

Statement 2 alone: While statement 2 provides information about the diagonal AC dividing the quadrilateral into two congruent triangles, it does not directly provide information about the angles or sides of the quadrilateral to determine if it is a parallelogram. Hence, statement 2 alone is not sufficient.

Combined Analysis:
When we combine both statements, we can see that statement 1 already tells us that the quadrilateral is a parallelogram. Additionally, statement 2 provides further information about the division of the quadrilateral into two congruent triangles, but this information is not necessary to determine if the quadrilateral is a parallelogram.

Therefore, the correct answer is option 'A' - Statement (1) alone is sufficient to answer the question asked.
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Is quadrilateral ABCD a parallelogram?(1) All four internal angles of ABCD are equal.(2) AC, a diagonal of ABCD, divides ABCD into two congruent triangles.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer?
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Is quadrilateral ABCD a parallelogram?(1) All four internal angles of ABCD are equal.(2) AC, a diagonal of ABCD, divides ABCD into two congruent triangles.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Is quadrilateral ABCD a parallelogram?(1) All four internal angles of ABCD are equal.(2) AC, a diagonal of ABCD, divides ABCD into two congruent triangles.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Is quadrilateral ABCD a parallelogram?(1) All four internal angles of ABCD are equal.(2) AC, a diagonal of ABCD, divides ABCD into two congruent triangles.a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer?.
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