Q1
In a triangle, the sum of any two sides must be:
Agreater than the third side
Bequal to the third side
Cless than the third side
Dexactly double the third side
CBSEClass 9 (CBSE)MathematicsCh 7 · Topic 2
Properties of Triangles
Learning key inequality and angle properties of triangles.
Core concept
This triangle inequality can be checked quickly: for sides 3, 4, 5, we verify 3+4>5 (7>5, true), 3+5>4 (true), and 4+5>3 (true) — all conditions hold, so a valid triangle can be formed. If any one of these conditions fails (like trying to form a triangle with sides 2, 3, 6, where 2+3=5 is NOT greater than 6), no valid triangle exists — the two shorter sides simply cannot 'reach' to close the triangle shape.
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• Triangle inequality: the sum of any two sides must be greater than the third side.
• The angle opposite the longest side is the largest angle in the triangle.
• Sides 3,4,5 satisfy the triangle inequality (3+4>5, etc.) and can form a valid triangle.
• Sides 2,3,6 fail the inequality (2+3 is not >6) and cannot form a valid triangle.