Question

In \( \triangle ABC \), \( DE \) is a line such that \( \frac{AD}{DB} = \frac{AE}{EC} \) and \( \angle EDA = \angle ACB \), then \( \triangle ABC \) is a/an:

• A. Scalene triangle
• B. Isosceles triangle
• C. Equilateral triangle
• D. Right-angled triangle

Hint:

If a triangle has an angle bisector that divides the opposite side in a specific ratio, the triangle is likely isosceles.

Answer 1

The Correct Option is B

We are given that \( \frac{AD}{DB} = \frac{AE}{EC} \) and \( \angle EDA = \angle ACB \). From the Angle Bisector Theorem, we know that if a line divides two sides of a triangle proportionally, then the triangle must have some symmetry. Here, since the angle bisector of \( \angle ACB \) divides the sides in equal ratios, it indicates that \( \triangle ABC \) is isosceles. Thus, the triangle is isosceles because two sides, \( AB \) and \( AC \), are equal due to the proportionality condition and the angle bisector condition.