Question
Which of the following relation is correct if AD = AC?
- AB < AD
- AB > AD
- AB = AD
- AB =
AD
AD
Hint:
According to the properties of a triangle, the side opposite to larger angle is longer than the side opposite to the smaller angle and Angles opposite to equal sides are equal. using statement compare the two sides AB and AC of the triangle ABC.
The correct answer is: AB > AD
In ΔACD, AD = AC
⇒ ∠ADC = ∠ACD ————–(i) (Angles opposite to equal sides are equal)
⇒ ∠ADC = ∠ACB ————–(ii)
Since, the exterior angle of a triangle is greater than each of the interior opposite angles,
∠ADC > ∠ABD
⇒ ∠ACB > ∠ABC (From equation ii)
⇒ AB > AC (Side opposite to larger angle is the longer side in a triangle)
⇒ AB > AC (AD = AC).
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