D is any point on side BC of triangleABC,such that AD=AC show that AB AD - Maths - Triangles

Question

D is any point on side BC of triangleABC,such that AD=AC show that
AB>AD

Lovina Kansal · Accepted Answer

Dear student
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In △ADC, we haveAD=AC   [Given]⇒∠ACD=∠ADC   [Angles opposite to equall sides are equal]   
(1)In △ABD, BD is produced to C and exterior angle of triangle is greater than each of interior opposite angle
∴ Ext
 ∠ADC>∠ABD    
(2)From (1) and (2), we have∠ACD>∠ABD⇒∠ACB>∠ABC   [∵∠ACD=∠ACB and ∠ABD=∠ABC]Thus, in△ABC, we have∠ACB>∠ABC⇒AB>AC   [∵Side opposite to greater angle is larger]But, AC=AD   [Given]∴AB>AD

D is any point on side BC of triangleABC,such that AD=AC.show that AB>AD