Should their be an SSA Postulate?

Look at the diagram shown here. Which segments are congruent? Which angles are congruent?

Note on All Multiple Choice!

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Which congruence pattern applies to this diagram?

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Can you change the length of AB?

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Can you move point F?

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Can you change the length of DF?

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Can you change the length of BE?

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What else changes when you move point E? Be specific.

What happens when you adjust the slider labeled k?

Now move point E so that it lands somewhere on the long ray extending from point A and makes a triangle.

IS CDF a triangle now? Explain.

Rotate point F so that it lands on the ray extending from point C to complete triangle CDF.

Is triangle CDF congruent to triangle ABE? Justify your answer.

Try to find another point on the ray to put point F so that it forms a different triangle. Can you do it? Explain.

Experiment with different values of k (the angle slider), lengths of BE, and positions of point F. Try to make two triangles which satisfy the SSA criteria but are NOT congruent.

Can you make two triangles satisfy the SSA criteria but are not congruent? How? List the side and angle values for each triangle.

Can you find a combination of angle measures and side lengths where the triangles do have to be congruent, i.e. there is only one possible place to put point F and it makes a triangle that is congruent to ABE? Explain how and give the side/angle measures for your triangles.

Should geometry include an SSA Postulate for triangle congruence? Justify your answer.