Question

if a perpendicular is drawn from the vertex of right angle of right triangle to the hypotenuse,then prove that the triangles on both the sides of perpendicular are similar to the whole triangle and to eachother​

Answer 1

In ∆ ADB and ∆ ABC

A= A ( commom )

ADB = ABC ( each 90°)

Hence. ∆ ADB ~ ∆ ABC ( BY AA ) .……...(1)

similarly :

In ∆ BCD & ∆ ABC

C= C ( common )

BCD = ABC ( each 90°)

hence

∆ BCD ~ ∆ ABC ( by AA).……..(2)

FROM eq. (1) and (2).

∆ ADB~∆ ABC & ∆ BDC ~∆ ABC .

NOTE: If one ∆ is similar to another and

second ∆ is similar to third ∆

then first and third ∆ are similar

hence :

∆ ABD ~ ∆ BCD

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