Which of the following statements must always be true of two similar non congruent triangle?
None of the above.
Two similar non congruent triangles will always have the following properties:
1. Corresponding angles are congruent: This means that the angles that have the same position in each triangle are equal in measure. To verify this, you can compare the corresponding angles of the two triangles. If they are equal, then the statement holds true.
2. Corresponding sides are proportional: This means that the lengths of the corresponding sides of the triangles are proportional. To check this, you can divide the length of one side of the first triangle by the length of the corresponding side of the second triangle. Repeat this for each pair of corresponding sides. If the ratios of these lengths are equal, then the statement is true.
By checking these two properties, you can determine if two non congruent triangles are similar. However, it is important to note that being similar does not mean the triangles are congruent, as congruence requires both sides and angles to be equal. Similarity only guarantees the proportional relationships between corresponding angles and sides.