SOLUTION: If ΔDEF and ΔJKL are two triangles such that ∠D ≅ ∠J, which of the following would be sufficient to prove the triangles are similar?

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Question 1064742: If ΔDEF and ΔJKL are two triangles such that ∠D ≅ ∠J, which of the following would be sufficient to prove the triangles are similar?
Found 2 solutions by jim_thompson5910, ikleyn:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Take note how
D and J are the first letters of the letter sequences
E and K are the second letters of the letter sequences
F and L are the third letters of the letter sequences

This order and correspondence is important.

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We are given ∠D ≅ ∠J

To prove the two triangles similar, there are two scenarios possible.

Scenario 1: If we knew that ∠E ≅ ∠K, then we have enough to add to the initial facts to prove that the triangles are similar.

OR

Scenario 2: If we knew that ∠F ≅ ∠L, then we have enough to add to the initial facts to prove that the triangles are similar.

There are no other scenarios possible. Only one of the scenarios needs to be shown (not necessarily both at the same time). Recall that the Angle Angle (AA) Similarity Theorem only needs two congruent pairs of angles. We don't need all three.

Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
1.   ". . . which of the following would be sufficient to prove the triangles are similar?"

      Nothing follows.


2.  On triangles similarity see the lessons
    - Similar triangles
    - Similarity tests for triangles
    - Proofs of Similarity tests for triangles
    - In a triangle a straight line parallel to its side cuts off a similar triangle
    - Problems on similar triangles
in this site.