- ABC (opposite ∠A)
- BAC (opposite ∠B)
- CAB (opposite ∠C)
- DCannot be determined
Step-by-Step Solution
∠C = 180 − 80 − 60 = 40°. Largest angle = ∠A (80°). The side opposite ∠A is BC, so BC is the longest.
Answer: A) BC (opposite ∠A)
In ΔABC, ∠A = 80° and ∠B = 60°. Which side is the longest?
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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