Question

Triangle ABC and Triangle PQR are congruent.
(I) Area of triangle ABC and triangle PQR are same
(II) Triangle ABC and triangle PQR are right angle triangles.

• A. Data in Statement I alone is sufficient to answer the question but the data in Statement II alone is not sufficient to answer the question.
• B. Data in Statement II alone is sufficient to answer the question but the data in Statement I alone is not sufficient to answer the question.
• C. Data in statements I and II together are necessary to answer the question.
• D. Data in statements I and II together are not sufficient to answer the question.

Answer 1

The Correct Option is D

The question determines whether the given data statements are sufficient to conclude anything about the congruent triangles ABC and PQR.

1. Triangle ABC and Triangle PQR are congruent. Congruent triangles have equal areas, so Statement I confirms their areas are the same. However, this is already a property of congruent triangles and provides no new insight. 
2. Statement II states that both triangles are right triangles. Knowing they are right triangles and congruent implies equal corresponding angles and sides, but again, this information does not independently aid in any further deductions about a specific question other than what congruence already dictates.

Evaluating the options, neither statement independently helps ascertain anything beyond the provided data or known geometric properties of congruent, right triangles. Therefore, the two statements together cannot provide additional insights or answers. Hence, the correct choice is:

Data in statements I and II together are not sufficient to answer the question.