Friday, August 3, 2012

Right Similar Triangles

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.” This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com

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