Question

18. The vertical
angle
A of an
of an isosceles.
triangle ABC is 70. which of the following
relations is correct.
(a) AB > BC (B) AB is less thanAC (C) AC is greater than BC (D) AC<BC​

Answer 1

Step-by-step explanation:

In ∆ABC,

We have:

AB = AC⇒∠ACB = ∠ABC

[Angles opposite to equal sides are equal] ....(1)

We know that exterior angle of a ∆ is always greater than each of the interior opposite angle.

In ∆ADC,

∠ADB > ∠ACD

⇒∠ADB > ∠ABD [Using (1)]

⇒AB > AD

[Sides opposite to greater angle is longer]

⇒AC > AD [As, AB = AC] .....(2)

We know that exterior angle of a ∆ is always greater than each of the interior opposite angle.

In ∆ACE,

∠ACD > ∠AEC

⇒∠ABE > ∠AEB [Using (1)]

⇒AE > AB

[Sides opposite to greater angle is longer]

=> AE > AC [As, AB=AC].......... (3)

From (2) & (3) we get,

AE > AD