SOLUTION: Which of the following conditions cannot be used for checking that two triangle are congruent? (1) two corresponding angles and corresponding sides are equal (2) two correspondin

Question 499182: Which of the following conditions cannot be used for checking that two triangle are congruent?
(1) two corresponding angles and corresponding sides are equal
(2) two corresponding sides and the corresponding included angles are equal
(3) three corresponding angles are equal
(4) three corresponding sides are equal
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
answer is (3)
3 angles are congruent proves that the triangles are similar.
they are not necessarily congruent.
their corresponding sides are in proportion to a common ratio.
only if the common ratio is 1:1 will they be congruent.
example:
triangle 1 and triangle 2 have equal angles all around.
their corresponding sides are in the common ratio 1:2
this means that the lengths of the sides of triangle 2 are 2 times the lengths of the corresponding sides of triangle 1.
the triangle are similar.
their angles are equal and their sides are in proportion.
if the common ratio was 1:1 then the sides would be congruent and the triangles would be congruent.

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