Question

Which of the following must be true? fan and medal
A. BCED C.BC= ED D. BC<=ED

Answer 1

@AlexandervonHumboldt2 @alyssa_michelle1996 @DanJS @satellite73 @mathmate

Answer 2

Hint:

If lengths a, b and \(\angle A\) are known, \(c^2=a^2+b^2-2~a~b~cos(C)\)
In the given problem, a and b are known (therefore constant), and cos(C) is a decreasing function, so as \(\angle\)C increases, c^2 increases as well.

Answer 3

I don't buy C as the answer.

One, if BC=ED then the alternate interior angles would be equal. However 24 degree does not equal 30 degrees.

Two, the side opposite the 24 degree angle has to be smaller then the side opposite the 30 degree angle. So once again, BC can not equal ED.

Answer 4

They cannot be equal also because
if BC=ED then the two triangles would be congruent (SSS) and therefore \(30^\circ=24^\circ\) which is absurd.
The person who suggested equality has since deleted his/her post.

Anyway, in the current case, the length of the opposite side increases/decreases with the angle, so that the answer may be deduced accordingly.