Question

Im studying for a test. Can someone help me with this question? If AB = 10, what is the length of DE?

Answer 1

@ganeshie8 @phi @Callisto can you help me with this?

Answer 2

Draw lines from E to A and from D to E.

Answer 3

What is true of angle EAB and angle EDB?

Answer 4

Are they equal?

Answer 5

i thought that i would need to set up a proportion to solve this but Im getting confused about what proportion to set up

Answer 6

I won't prove the theorem here, but yes, they are called angles subtended by the same arc, meaning the arc from E to B.

So what is true of angle ACE and angel DCB?

Answer 7

they are equal

Answer 8

So triangles EAC and BDC are ____________?

Answer 9

congruent?

Answer 10

No. Congruent means exactly the same, so you could cut out one and set it on the other, and neither would overlap. But this is next best.

Answer 11

The are similar. Which means that corresponding lengths are proportional. The only thing you need to do is figure which parts are corresonding. You know that the angles at C are equal, and each of the trianges has a short leg and a long leg starting at C. So the short leg of one versus the short leg of the other must be in proportion to the long legs of the repsective triangles.

Answer 12

Either:

short leg of one/long leg of one = short leg of the other / long leg of the other

or

short leg of one / short leg of the other = long leg of one / long leg of the other

Either way will work.

Answer 13

oh gotcha, so it would be 6/8 = x/4 = 24=8x. then divide both sides by 8 to get x=3. and add 3 to 8 to get the length of the whole side?

Answer 14

Checking it the other way

3 / 4 ? 6 / 8
Seems to be true, so yes. 11 is the total length.

Answer 15

Whoops! The other way would be 3/6 = 4/ 8, but it is still true.

Answer 16

Thank you so much