Q1
What side is opposite the largest angle?
AThe longest side
BThe shortest side
CAny side, no relationship
DNo specific side
ICSEClass 9 (ICSE)MathematicsCh 11 · Topic 1
Inequalities
Inequalities in triangles relate side lengths and angles, showing that a larger angle is opposite a longer side, and vice versa.
Core concept
In any triangle, the side opposite the largest angle is the longest side, and the side opposite the smallest angle is the shortest.
How it works
The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side.
Why it matters
This means we can determine if three given lengths can form a triangle by checking if this condition holds for all three combinations.
Key detail
Understanding these inequalities helps us solve problems involving triangle properties and verify if a triangle can exist with given measurements.
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Quick notes
• The longest side is opposite the largest angle.
• The shortest side is opposite the smallest angle.
• Triangle inequality: sum of two sides > third side.
• This must hold for all three side combinations.
• This determines if a triangle can form.
• These relationships apply to any triangle.
• They help verify triangle measurements.
• This is a fundamental geometry concept.