To show that two triangles are the same using coordinates, you can use a few handy tricks:

1. Distance Formula: Use the distance formula, which is $d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$. This helps you find the lengths of the triangle’s sides. If all three sides of both triangles have the same lengths, then the triangles are congruent.

2. Midpoint Formula: Look for the midpoints of the sides. If the midpoints are the same for both triangles, this can help prove that they are congruent, especially if the triangles are isosceles (where two sides are equal).

3. Slope: Find the slopes of the sides of the triangles. If the slopes are the same, it can tell you about the angles. Matching slopes can show whether the triangles are similar or congruent.

Using these methods will make it easier to understand and check if the triangles have the same properties!