# Thread: Finding the length of a side of a triangle:

1. ## Finding the length of a side of a triangle:

In the above triangle ABC, line segment AD is 6, and I'm supposed to find the length of side BC.

I know I'm missing some basic knowledge about properties of triangles, or else this wouldn't completely baffle me.

Any help would be greatly appreciated.

2. Originally Posted by thumpin_termis

In the above triangle ABC, line segment AD is 6, and I'm supposed to find the length of side BC.
...
Hello,

I've modified your drawing a little bit so you can see how I did this problem:

(< this sign means angle):

<(CDB) = 2x° ==> <(ABD) = x°

Therefore triangle BAD is an isoscele triangle with the base AB. Thus AD = DB.

Triangle DCB is an isoscele triangle with the base DC. Thus DB = BC.

That means: 6 = AD = DB = BC

3. Hello, thumpin_termis!

Earboth is absolutely correct.
. . Here's the reason behind his solution.

Angle BDC = 2x is an exterior angle of triangle ABD.
. . Hence, it is the sum of the two non-adjacent angles.

That is: ./BDC .= ./BAD + /ABD

Hence: . . . 2x .= .x + /ABD

Then: . . /ABD .= .x

Therefore, triangle ABD is isosceles, BD = AD = 6, etc.

4. Awesome.

So lemme just make sure here:
/ABD = x can be found from the original information given, since /BDC=./BAD + /ABD would be true in such situations. Did I get that right?

5. Originally Posted by thumpin_termis
Awesome.

So lemme just make sure here:
/ABD = x can be found from the original information given, since /BDC=./BAD + /ABD would be true in such situations. Did I get that right?
Hello,

you got it.

Have a look at Soroban's post.
The exterior angle of a triangle is as great as the two non-adjacent angles of the triangle.

You can proof this "theorem" by using that the 3 angles in a triangle sum up to 180° and that a straight line forms an angle of 180° too.

6. Fantastic. Thank you very much guys.

7. Originally Posted by CaptainBlack
There is insufficient information. The diagram looks like AD=DB but you
cant assume that, it must state it.

RonL
angle 2x (D) = angle x (A) + angle () B .......... property of external angle to triangle
hence angle B = x
hence side AD = Side BD
Similarly angle BDC = Angle BCD
hence side BD = Side BC = 6