Question

Which conclusion is most likely correct about the figure?

The side AC is shorter than the side CD.

The measure of angle BCD is greater than the measure of angle BCA.

The measure of angle BDC is greater than the measure of angle BAC.

The side AC is equal to the side CD.

Answer 1

so, which one do you think?

Answer 2

D @jdoe0001

Answer 3

usually the wider the angle, the wider opening will make, well, a WIDER opening, than the narrower
all this assuming AB and BD are equal, so can't be D

Answer 4

so C then :o

Answer 5

well, I'd think that C is being bisected by 2 equal angles
that means that BDC is 180-(45- THAT ANGLE)
and BAC is 180-(40 - THAT ANGLE)
so, they can't be equal, so no dice on C either

Answer 6

hmm, maybe C has 2 different angles really, still doesn't make BDC and BAC equal

Answer 7

anyway from the picture, the 45 degrees angle, makes a WIDER opening, and thus a LONGER side on the other end, than the 40 degrees one
so, we could say that due to one angle at B being WIDER than the other
AC is shorter than CD

Answer 8

Here is the theorem needed for solution:

SAS Inequality/Hinge Theorem
If two sides of a triangle are congruent to two sides of another triangle and the included angle in one triangle has a greater measure than the included angle in the other, then the third side of the first triangle is longer than the third side of the second triangle.