- A2 cm, 3 cm, 6 cm
- B5 cm, 5 cm, 9 cm
- C1 cm, 2 cm, 3 cm
- D4 cm, 4 cm, 8 cm
Step-by-Step Solution
For 5, 5, 9: 5 + 5 = 10 > 9 ✓. The others fail: 2+3=5<6; 1+2=3 (not >3); 4+4=8 (not >8).
Answer: B) 5 cm, 5 cm, 9 cm
Which set of side lengths can form a triangle?
Class 9Triangles (Congruence)Geometry — Triangles
Key idea: Inequalities in a triangle
**Property 1**: In a triangle, the side opposite the LARGER angle is LONGER. (Bigger angle stretches the opposite side.)
**Property 2**: Conversely, the angle opposite the longer side is larger.
**Property 3 (Triangle Inequality)**: The sum of any two sides of a triangle is GREATER than the third side.
This means three given lengths form a triangle ONLY IF each pair sums to more than the third.
Example: Can 2, 3, 6 form a triangle? Check: 2 + 3 = 5 < 6. NO.
**Property 2**: Conversely, the angle opposite the longer side is larger.
**Property 3 (Triangle Inequality)**: The sum of any two sides of a triangle is GREATER than the third side.
This means three given lengths form a triangle ONLY IF each pair sums to more than the third.
Example: Can 2, 3, 6 form a triangle? Check: 2 + 3 = 5 < 6. NO.
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