Question

which of the triangles cannot be proved congruent? so a different tutor gave me the answer which is D. But he told me to ask another tutor to tell me how to type out how I got the answer.

Answer 1

The triangles that cannot be proved congruent are the triangles in option D. We are not told that the other side is congruent to the corresponding side of the other triangle.

To prove they are congruent, we need to know the other side is congruent and prove this using the SSS postulate.

In the other cases, we can be proved they are congruent by:

• Case A ---> SAS postulate.

,

• Case B ---> ASA postulate.

,

• Case C ---> SSS postulate (the triangles share a common side)

In summary, we only have that the triangles in D cannot be proved congruent since we have two corresponding congruent sides, and one angle (vertical angle) to be congruent corresponding parts. It would be an SSA method. However, this method is not Universal, and it is not enough to demonstrate they are congruent.