Question

In triangle angle BAC equal to 90 degree and ad perpendicular to BC then

Answer 1

Answer:

PROOF: <CAD + <DAB = 90 deg (given)

Also, < DAB + <DBA = 90 deg ( as given that triangle ADB is a right triangle)

=> <CAD + <DAB = <DAB + <DBA ( by above 2 statements)

=> <CAD = <DBA …………………. (1)

Similarly, <ACD = <DAB ……………(2)

=> triangle ADC ~ triangle BDA ( by AAA similarity criterion)

=> AD/BD = DC/AD ( corresponding sides of similar triangles)

=> AD^2 = BD x CD ( by cross multiplying)

[Proved]