Question

AD bisects ∠BAC. Sides of ABD arranged in descending order:

Options

• BD > AD > AB

• AB > AD > BD

• BD > AD > AB

• AD > AB > BD

Answer 1

AB > AD > BD

Explanation:

Given:

• In triangle ΔABC, AD bisects ∠BAC and we’re focusing on triangle ΔABD.

From the Angle Bisector Theorem, we know that a bisector divides the opposite side in the ratio of the adjacent sides. However, for ordering sides in triangle ΔABD, we use this:

In any triangle, the side opposite the larger angle is longer.

Since AD bisects ∠BAC, angles ∠BAD and ∠CAD are equal. But we are dealing with triangle ΔABD, where:

• ∠ABD is opposite side AD
• ∠ADB is opposite side AB
• ∠BAD is opposite side BD

Since AB is the full side of the main triangle and AD is just a bisector, generally:

AB (opposite ∠ADB) > AD (opposite ∠ABD) > BD (opposite ∠BAD)