Question: Is triangle \Delta right angled?<br>Statement I: The length of the line segment joining the mid-points of two sides of \Delta is half of the third side of \Delta.<br>Statement II: The angles of \Delta are in the ratio 1:2:3.
For the next ten (10) items that follow:<br>Each item contains a Question followed by two Statements. Answer each item using the following instructions:
- A. Choose this option if the Question can be answered by one of the Statements alone but not by the other. ✓
- B. Choose this option if the Question can be answered by either Statement alone.
- C. Choose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
- D. Choose this option if the Question cannot be answered even by using both Statements together.
Correct Answer: A. Choose this option if the Question can be answered by one of the Statements alone but not by the other.
Explanation
Statement I is the Midpoint Theorem, which applies to ALL triangles. It gives no specific information about angles. Statement II implies angles are 30^{\circ}, 60^{\circ}, 90^{\circ}, which means the triangle IS right-angled. Only Statement II alone can answer the question.
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