Q.1- ABC is a right triangle, right angled at C. If p is the length of the perpendicular from C to AB & AB=c, BC=a & AC=b. Prove that (i)pc=ab, (ii)1/p2=1/a2+1/b2.
Q.2- PRQ is a right triangle, right angled at Q. S & T are points on QR such that QS=ST=TR. Prove that 8PT2=3PR2+5PS2.
Q.3- AD is the bisector of angle BAC of triangle ABC. The length of BC=a, AC=b & AB=c. Prove that BD=ac/b+c, CD=ab/b+c.
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Q.5- IN triangle ABC, XYllBC & it divides triangle ABC into two parts of equal area. Find BX/AB.
Q.6- If A is the area of a right angled triangle & 'b' is one of the sides containing right angle. Prove thet the length of altitude on the hypotenuse is 2Ab/(under root)b4+4A2.
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5.
Ar (Δ AXY) = Ar (trapezium BCYX)
⇒Ar (Δ AXY) + Ar (Δ AXY) = Ar (Δ AXY) + Ar (trapezium BCYX)
⇒2 Ar (Δ AXY) = Ar (Δ ABC)
In Δ AXY and Δ ABC,
∠AXY = ∠ABC [Since, XY || BC, so ∠AXY and ∠ABC are corresponding angles]
∠A = ∠A
∴ Δ AXY ∼ Δ ABC
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