If two angles of one triangle are congruent to two angles of a second triangle,

then the third angles are congruent.


 A                                D

/\                               /\
/  \                             /  \
/     \                          /     \
 /____\                       /____\
                      B        C                    E       F                      

1.     /  A = /  D                                                         1.     Given

2.     /  B = /  E                                                          2.     Given

3.     /  A + /  B + /  C = 180                                     3.     Triangle Sum Theorem.

4.     /  D + /  E + /  F = 180                                       4.     Same.

5.     /  A + /  B + /  C = /  D + /  E + /  F                    5.     Substitution

6.     /  A + /  B + /  C = /  A + /  B + /  F                    6.     Substitution

7.     /  C = /  F                                                            7.     Subtraction

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