Question

If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse then the triangles on both sides of the perpendicular are similar to the whole triangle and also to each other .
Prove -
1 . ∆DBA ~ ∆ ABC
2. ∆ DAC ~∆ ABC
3. ∆ DBA ~ ∆ DAC

Answer 1

proof:


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



PROVED

Answer 2

$\red{HEY\:MISS!!}$

HERE'S THE ANSWER..

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♠️ Refer the attachment and refer the figure .

HOPE HELPED..

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