Theorem 6.7
If a perpendicular is drawn from the vertex of right angle of a right triangle to the hypotenuse then triangle on both side of the perpendicular are similar to the wall triangle and to each other.
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Theorem 6.7
If a perpendicular is drawn from the vertex of right angle of a right triangle to the hypotenuse then triangle on both side of the perpendicular are similar to the wall triangle and to each other.
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Step-by-step explanation:
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