Prove that triangle ABC is isosceles if any one of following holds.
(1) altitude AD bisects .
(2) median AD is perpendicular to the base BC.
No Spam ❌
(1) altitude AD bisects .
(2) median AD is perpendicular to the base BC.
No Spam ❌
Add an Answer
More Questions From This User See All
Answers & Comments
Given :-
(1) In ∆ ABC altitude AD bisects BC.
(2) AD is perpendicular to BC.
To prove :-
∆ ABC is an isosceles ∆.
Proof :-
In ∆ ABD and ∆ ACD :-
AD = AD (common)
BD = CD (AD bisects BC)
<ADB = <ADC (each are of 90° because AD is perpendicular to BC)
so,
∆ ABD ≈ ∆ ACD (SAS)
AB = AC (by CPCT)
now,
In ∆ ABC
AB = AC
so, ∆ ABC is an isosceles ∆.
I hope it helps uh ra Mello ✨