Plzz help with the following questions:(plzz little fast)
1) if one diagonal of a trapezium divides the other diagonal in the ratio 1:3.prove that one of the parallel sides is three times the other.
2)triangle ABC is an equilateral triangle .Find the ratio of the area of the equilateral triangle described on a side of the triangle to the area of the equilateral triangle decribed on one of its altitude.
3) in figure, ABC is a right triangle , right angled at CC.let BC=a, CA=b, AB=c and leot p be the length of perpendicular from C on AB.prove that:
i) cp=ab
ii)1/p^2=1/a^2+1/b^2
Plzz help fast
if one diagonal of a trapezium divides the other diagonal in the ratio 1:3.prove that one of the parallel sides is three times the other.
It is given that one diagonal (BD) divides the other diagonal (AC) in the ratio 1:3
So, OC/AO = 1/3.
We should prove that DC = 3 (AB)
We have ,
∠AOB = ∠COD (because they are vertically opposite angles)
and
∠ABO = ∠ODC (Since CD||AB, BD is a transversal and these are alternate angles).
So, By AA we can say the triangles AOB and COD are similar.
So, the sides of these triangles are in proportional.
OC/AO = DC/AB
1/3 = DC/AB
DC = 3 (AB)