In the following applet , let triangle PQR be a right triangle, right angled at Q. Let QS be the perpendicular to the hypotenuse PR.
From ΔPSQ and ΔPQR, we have ∠P = ∠P,
∠PSQ=∠PQR(both 90°) ,
so ΔPSQ ∼ ΔPQR ( By AA Criteria)
Similarly , ΔQSR ∼ ΔPQR.
So , ΔPSQ ∼ ΔQSR , thus we can say that
“ If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.”
∠PSQ=∠PQR(both 90°) ,
so ΔPSQ ∼ ΔPQR ( By AA Criteria)
Similarly , ΔQSR ∼ ΔPQR.
So , ΔPSQ ∼ ΔQSR , thus we can say that
“ If a perpendicular is drawn from the vertex of the right angle of a right triangle to the hypotenuse then triangles on both sides of the perpendicular are similar to the whole triangle and to each other.”
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