Answer: D
Step-by-step explanation:
To find which of the conditions is not sufficient to show that the two triangles are congruent (same size and shape), let's analyze the options.
Option A.
The lengths of corresponding sides are equal...
--> If the lengths of corresponding sides in a triangle are equal, this is sufficient to show that the triangles are congruent.
Option B.
The rise and run of the translation between each pair of corresponding points are the same.
--> The rise and run is the slope of the lines between the points, if the slopes between corresponding points are equal, that is sufficient to show that the triangles are congruent.
Option C.
Each vertex of ABC corresponds to a vertex of XYZ after translating 5 units right and 7.5 units down.
--> If XYZ is the result of translating the vertex of ABC across the plane, the triangles are congruent, this option is also sufficient to show that the triangles are congruent.
Option D.
ABC and XYZ have the same orientation.
--> Two triangles can have the same orientation but to be congruent, their sides and angles must also be the same. Thus, orientation alone is NOT sufficient to show that the triangles are congruent.
Answer: D