the last choice is not clear it is,

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Oct 27th, 2015

Thank you for the opportunity to help you with your question!

The first thing to do is look at the order of the letters in each triangle. The order of the letters tell us the order of the points in a clockwise order. This is important because when we say that two triangles are congruent, we can say that their individual parts are congruent too. BUT THEY HAVE TO BE IN THE SAME SPOT IN THE ORDER OF LETTERS. So, side AB is congruent to side EF, because these letters are in the same spots. AC is congruent to EG, because the letters match up in the same spots. Now, the order matters for angles too. To better see how this works, it is best to draw two triangles and label them. Notice that I write the letters in order going clockwise.

                   A                                                                  E
 
           C              B                                                G              F
Now, we can look at the angle choices available. Draw the angle CBA, starting at point C and ending at A. Now draw the angle GEF, starting at G and ending at F. Notice that you did not dra the angle in the same direction both times. They are different angles and are not congruent. Now draw the angle BAC, starting at B and ending at C. Also draw angle FEG, beginning at F and ending at G. Did you draw the angle in the same direction both times? This means that these angles are congruent.
The correct answer then is <BAC is congruent to <FEG

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 27th, 2015

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