Observe the figure below.
Statement Reason
1. AC and BD bisect each other Given
2. AE = EC and BE = ED Definition of bisection
3. 
Vertical angle theorem
Vertical angle theorem states " When two lines intersect each other, the vertically opposite angles are always equal".
4. 
SAS criterion for congruence
5. 
Corresponding angles of congruent triangles are congruent
6. 
Converse of alternate interior angle theorem
7. 
Vertical angle theorem
8. 
SAS criterion for congruence
9. 
Converse of alternate interior angle theorem
As, , so 
as corresponding parts of corresponding triangles are equal. As these angles are alternate interior angles, so the lines BC and AD are parallel by "Converse of alternate interior angle theorem".
1) Never heard of someone referring to the Law of Levers before, must be showing my age. A system as you describe is at equilibrium when the net torque is equal to zero. Since torque is Fr=mgr so for this system we have a sum of:
27g*10+30g*x=0 The sum must be zero to be at equilibrium, dividing both sides by g you have:
270+30x=0
270=-30x
x=-9
The negative just indicates that the magnitude of 9 is on the opposite side of the fulcrum, so x=9ft in magnitude.
2) Inverse variation is of the form y=k/x, in this case we are given a point so we can solve for the constant, k, of variation...
y=k/x, and we are given y=-12 when x=5 so
-12=k/5
k=-60 so the equation is:
y=-60/x which can be expressed as
xy=-60
Hello,
This number is already in stranded form.
If you want it in scientific notation its : 5.4003*10^6
Hope this helps a bit.
