In Δ ABC, if AB AC then:

Question

In Δ ABC, if AB AC then:

1. A. ∠B ∠C
2. B. ∠B = ∠C
3. C. ∠C ∠B (Correct answer)
4. D. None of the above

Correct Answer

Option C — ∠C ∠B

Detailed Solution & Explanation

The correct answer is ∠C > ∠B.

Key Points

• In any triangle, the larger side lies opposite the larger angle.
• Side AB is opposite ∠C, and side AC is opposite ∠B.
• Since AB > AC, it follows that ∠C > ∠B.

Additional Information

• The converse also holds: the greater angle has the greater side opposite it.
• Identifying which angle faces which side is the whole difficulty — the side is always named by the two vertices it joins, and the opposite angle is the third vertex.
• Related result: the triangle inequality, which requires the sum of any two sides to exceed the third.