SOLUTION: Sir, This is quenstion on congruence of Triangles.ABC is a triangle in which AD is the bisector of angle A. If AD is perpendicular to BC, show that triangle ABC is Isoscele. Give r

Algebra ->  Triangles -> SOLUTION: Sir, This is quenstion on congruence of Triangles.ABC is a triangle in which AD is the bisector of angle A. If AD is perpendicular to BC, show that triangle ABC is Isoscele. Give r      Log On


   

Question 48762: Sir, This is quenstion on congruence of Triangles.ABC is a triangle in which AD is the bisector of angle A. If AD is perpendicular to BC, show that triangle ABC is Isoscele. Give reasons.
A
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B/----D-----\C
I tried it like this.
In triangle ABD and triangle ACD
(i) AD=DA (Common side)
(ii) Angle BAD=Angle CAD (by CPCT)
(iii)Angle ADB=Angle ADC=90 degree because AD Perpendicular to BC
Therefore triange ABD is congruent to triangle ACD by ASA congruency
Hence AB=AC and Triangle ABC is isoscele.
But I M not confident with my solution. PL. help me.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
i am rusty on congruency but if ASA is a test for it (which i believe it is) then your solution is perfect.

Well done
Jon