Help with Geometry Concept

[atlcharm]

I do understand you can assume nothing from the diagrams. My question is on the principles.

 

Here is the question which I've inserted in three photos

part 1: https://docs.google.com/file/d/0B8G2c7VPiWjoSnJjUHRWQ0NoLTA/edit?usp=sharing

 

part 2: https://docs.google.com/file/d/0B8G2c7VPiWjoUHpraDVkZVpRekE/edit?usp=sharing

 

part 3: https://docs.google.com/file/d/0B8G2c7VPiWjoYkxsZXBHWFNRZUU/edit?usp=sharing

 

My answer would have easily been C - that m and n are equal (the answer is D). I didn't assume that based on the pic. I assumed that because line AD and DC are equal. I thought that equal-sized lines had equal-sized angles. I'm getting this from all the rules on triangles and angles. For instance here:

 

https://docs.google.com/file/d/0B8G2c7VPiWjoMWlkZVBpYkExOVU/edit?usp=sharing

 

Can anyone help me get this straight in my head? I feel like a lot of this stuff is just memorization, but I'd like to make valid connections.

[gbd97]

Hi,

It looks like this is from Princeton review, right?

 

Actually C is trap answer here.

 

Actually the opposite angles of equal sides of a triangle are equal.(mind it of a Single triangle)

 

Here in the first case two sides are equal but that are from different triangle(AD from ADB triangle, DC from BDC triangle); so that formula will not work here.

 

For the second case, both sides are from a single triangle. So, the formula works here!!!!!!!