Warm Up 1.Name a chord 2.What term describes <QPR 3.Name an arc 4.What term describes TU 5.Name an intercepted arc 6.Name a tangent

9.3 Altitudes-on-Hypotenuse Theorem A B C D Altitude CD drawn to hyp. of △ ABC Three similar triangles are formed.

A B C D C A DC B D A C B Three similar triangles: small, medium and large.

A B C D Altitude-on-Hypotenuse Theorems Set up proportions!

T68: If an altitude is drawn to the hypotenuse of a right triangle then,  a. The two triangles formed are similar to the given right triangle and to each other. Δ ADC ~ Δ ACB ~ Δ CDB A B C D

 b. The altitude to the hypotenuse is the mean proportional between the segments of the hypotenuse. x= h or h 2 = xy h y A B C D h a b x y c

 C. Either leg of the given right triangle is the mean proportional between the hypotenuse of the given right triangle and the segment of the hypotenuse adjacent to that leg (ie…. the projection of that leg on the hypotenuse) y = a or a 2 = ycorx = b or b 2 =xc a cb c A B C D xy b a h