Question

ABC is a right angled triangle with AB=AC bisectors of angle angle A meets BC at D prove that BC=2AD

Answer 1

Answer:

In right angled at Laandge AB= AC

hence,

/A+/B+/C=180°

90°+/B+/B=180°

2/B=180°-90°

2/B=90°

/B=45°------------------(1)

Also,

AD is the bisector of BAC

so,/BAD=/CAD=90°/2=45°---------(2)

/BAD=/ABC

so,AD=BD----------(3)

similarly angle CAD=angleACD

so,AD=DC---------(4)

adding eqn (3)and(4)

we will get,

AD+AD=BD+DC

2AD=BC

HENCE PROVED......