Mathematics
Statement (1): AB = AC and D is any point on side BC of triangle ABC.
Statement (2): AB > AD.
Both the statements are true.
Both the statements are false.
Statement 1 is true, and statement 2 is false.
Statement 1 is false, and statement 2 is true.
Triangles
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Answer
Since AB = AC, ΔABC is an isosceles triangle.
The angles opposite to equal sides of a triangle are equal.
⇒ ∠B = ∠C
∠ADB is an exterior angle to ΔADC.
Therefore, ∠ADB > ∠C
⇒ ∠ADB > ∠B
⇒ AB > AD (Side opposite to the largest angle in a triangle is the longest side)
∴ Both the statements are true.
Hence, option 1 is the correct option.
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