Question

in triangle abc BAC is equal to 90 degree and AD perpendicular to BC prove that AC square is equal to BC into DC​

Answer 1

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Answer 2

Answer:

Proved

Step-by-step explanation:

in triangle abc BAC is equal to 90 degree and AD perpendicular to BC prove that AC square is equal to BC into DC​

Let say ∠CAD = x°

then ∠DAB = 90° - x°  ( as ∠BAC = 90°)

now in Δ BAD

∠DBA + ∠DAB  + ∠ADB = 180° ( sum of angles of triangle Δ)

∠ADB = 90° as AD ⊥ BC

∠DBA + 90° - x° + 90° = 180°

∠DBA = x°

∠DBA = ∠CBA   ( as d is point on straight line BC)

in Δ ABC   &  Δ ADC

∠BAC = ∠ADC = 90°

∠CBA = ∠DAC = x°

∠DCA = ∠BCA = common angle

so

Δ ABC ≅ Δ ADC

AC / BC  =  DC/AC   =  AD/AB

using first two

AC / BC  =  DC/AC

=> AC² = BC × DC

QED