Question

Prove that ABC is isosceles if any one of the following holds 1. Altitude AB bisects BC 2. Median AD is perpendicular to BC 3. Altitude be = altitude CF

Answer 1

Given: triangle ABC
Required to prove: ABC is isosceles, i.e. AB=AC
Proof: Using number 2) Median AD perpendicular to BC
In triangle ADB and triangle ADC
AD=AD ( given )
Angle ADB=Angle ADC ( as AD is perpendicular to BC )
BD=DC ( as D divides BC into two equal halves )
Therefore,
Triangle ADB congruent to Triangle ADC
=> AB=AC ( CPCT )
Therefore Triangle ABC is isosceles.
Hence proved.


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Answer 2

the first answer is right