Similar Triangle Question

[JenniferLovesMath]

I'm having a difficult time figuring this out out. It's from a chapter that has both similar triangle concepts and geometric mean. I cannot figure out what I am missing here. I've included work that I've done....

 

[Romsek]

I'm having a difficult time figuring this out out. It's from a chapter that has both similar triangle concepts and geometric mean. I cannot figure out what I am missing here. I've included work that I've done....

View attachment 3476

It looks to me that BD is intended to be perpendicular to AC. If this is the case then angle ADB is 90 deg. That means that ABC is 90 deg and the whole thing is a right triangle.

This gets you 3 equations via the pythagorean theorem applied 3 times

6^2 + BD^2 = BC^2

AB^2 + BC^2 = 8^2

2^2 + BD^2 = AB^2

3 equations, 3 unknowns, just solve for BD, BC, AB

 

[JenniferLovesMath]

It looks to me that BD is intended to be perpendicular to AC. If this is the case then angle ADB is 90 deg. That means that ABC is 90 deg and the whole thing is a right triangle.

This gets you 3 equations via the pythagorean theorem applied 3 times

6^2 + BD^2 = BC^2

AB^2 + BC^2 = 8^2

2^2 + BD^2 = AB^2

3 equations, 3 unknowns, just solve for BD, BC, AB

No, It's seems like it (from my picture), but BD is not Perpendicular with AC....
Any other ideas?

 

[JenniferLovesMath]

No, It's seems like it (from my picture), but BD is not Perpendicular with AC....
Any other ideas?

I have an idea about what the answer is, but I just want someone to confirm it...If I give the answer, then I might bias the result....

 

[stapel]

[Note: I'm using "m(x)" to mean "the measure of angle x".]

Doesn't m(DAB) have to be the same as m(CAB)? So then what can you say about the third angle in each of the two triangles (at the bottom of your drawing)?