Question

In the given figure, if AB > AC, then which of the following is true?

• A. AB < AD
• B. AB = AD
• C. AB > AD
• D. Cannot be determined

Answer 1

The correct option is C AB > AD

AB > AC [Given]
∴ ∠ACB > ∠ABC
[The angle opposite to the longer side of a triangle is larger.]

Now, ∠ADB > ∠ACD (= ∠ACB)
[By exterior angle property]

⇒ ∠ADB > ∠ACB > ∠ABC (= ∠ABD)
⇒ ∠ADB > ∠ABD
⇒ AB > AD
[The side opposite to the larger angle of a triangle is longer.]