Final Answer:
1) The triangles STU and KLM do not necessarily have the same area. 2) The triangles STU and KLM do not necessarily have the same perimeter. 3) The triangles STU and KLM do not necessarily have the same angle measures. 4) The triangles STU and KLM do not necessarily have the same side lengths.
Step-by-step explanation:
1) The area of a triangle is determined by the base and height. Without specific information about the side lengths and heights of triangles STU and KLM, we cannot conclude that they have the same area.
2) The perimeter of a triangle is the sum of its three sides. Without information about the side lengths, we cannot determine if the triangles have the same perimeter.
3) Triangles with the same angle measures are congruent, but the question doesn't provide information about the angle measures of STU and KLM, so we cannot conclude that they have the same angles.
4) For triangles to have the same side lengths, they need to be congruent. Without information on the side lengths or any congruence conditions specified, we cannot determine if the triangles have the same side lengths.
In conclusion, the properties mentioned (area, perimeter, angle measures, side lengths) cannot be assumed to be the same for triangles STU and KLM without additional information about their specific characteristics.