Question

What is the measure of AC?

Answer 1

Two quick questions on that:

1. Are any of the lines parallel that you know of?
2. Do you know if any of the points B,D, or F bisect the line segments they're on?

Answer 2

oh. B bisects AC

Answer 3

Ok. I'll see if I can find something for you...

Answer 4

D bisects EC and F bisects AE

Answer 5

ok

Answer 6

is the answer 38

Answer 7

Not necessarily. Only if the triangle is equilateral or isosceles (with EC and AC being the two congruent sides).

Answer 8

Well it doesn't exactly tell me that all it says is that points B, D, and F are midpoints of the sides of ^ACE, EC = 38 and DF = 16. But it looks like an equilateral triangle.

Answer 9

It's not equilateral. If it were then either FD would be 19 or EC would be 32

Answer 10

Well if its not an equilateral triangle what do i do to find AC?

Answer 11

Ah-hah!

If we consider the triangles EFD and ACE, we see that they both share the FED angle.

Then, since we know that DF bisects both AE and EC, we know that EF = 2 AE and ED = 2 EC.

Thus we can say that the triangles are similar.

Then we can say \[\frac{ ED }{ EC }=\frac{ FD }{ AC }\]Substituting in your know values you get \[\frac{ 19 }{ 38 }=\frac{ 16 }{ AC }\]So then you get \[AC=\frac{ 16 \times 38 }{ 19 }\]

Answer 12

so its 32?

Answer 13

Yes

Answer 14

ok thank you i just didnt get tht

Answer 15

:P