2023 · Q78
Item contains a Question followed by two Statements. Answer each item using the following instructions : Question : Is triangle right angled?
Statement IThe length of the line segment joining the mid-points of two sides of a triangle is half of the third side of the triangle.
Statement IIThe angles of a triangle are in the ratio 1 : 2 : 3
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AChoose this option if the Question can be answered by one of the Statements alone but not by the other.
- BChoose this option if the Question can be answered by either Statement alone.
- CChoose this option if the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
- DChoose this option if the Question cannot be answered even by using both Statements together.
Explanation
Statement I (the midpoint-segment theorem) holds for every triangle, so it carries no information about right-angledness. Statement II (angles in ratio 1:2:3, i.e. 30°, 60°, 90°) alone confirms the triangle is right-angled. The question is answered by one statement alone (A).