Carefully examine each diagram below and explain why the geometric figure cannot exist. Support your statements with reasons.

1. 

   Hint (a) - (c) and (f):

   Read the Math Notes box from Lesson 7.1.6 to review the triangle congruence conjectures.

   Answer (a):

   The triangles should be congruent by $\text{SSS} ≅$, but $80º ≠ 50º$ and in congruent triangles all angles are equal as well.

2. 

   Answer (b):

   The triangles should be congruent by $\text{SAS} ≅$, but $80º ≠ 90º$ and $40º ≠ 50º$ and in congruent triangles all angles are equal as well.

3. 

   Answer (c):

   The triangles should be congruent by $\text{SAS} ≅$, but $10 ≠ 12$ and in congruent triangles all sides are congruent as well.

4. 

   Hint (d) and (e):

   What do you know about isosceles triangles?