To determine if the triangles above are translations of each other, you must check to see if all of the triangles are exact copies of each other (congruent). [br][br]First, measure one of the triangles.[br] 1. Use the polygon tool to outline the triangle that is lowest in the picture (the darker blue one.)[br] 2. Use the distance tool to measure the side lengths.[br] 3. Use the angle tool to measure the angles.[br][br]Second, measure the next triangle above the first one (the lighter blue triangle), using the SSS Congruence Theorem.[br] 4. Use the polygon tool to outline the lighter blue triangle.[br] 5. Use the distance tool to measure the three side lengths of the lighter blue triangle.[br] 6. Are the lengths nearly the same as the three sides of the first triangle? If so, we can consider the  triangles congruent by the SSS Theorem without having to measure the angles of the triangle.[br][br]Third, measure the brown triangle using the SAS Triangle Congruence Theorem to see if it is congruent to the other two.[br] 7. Outline the brown triangle using the polygon tool.[br] 8. Use the distance tool to measure any two sides.[br] 9. Use the angle tool to measure the included angle (the angle in between the two sides you measured.) If the corresponding side lengths match and the included angle measure matches, then we can say the two triangles are congruent by the SAS Theorem without having to measure and compare the rest of the triangle parts. [br][br]Forth, measure the orange triangle using either the AAS or the ASA Theorems to see if it is congruent to the others.[br]10. Outline the orange triangle with the polygon tool.[br]11. Use the distance tool to measure any one side.[br]12. Use the angle tool to measure any two angles. If the corresponding side lengths match and the corresponding angle measures match, the two triangles are congruent by the AAS or the ASA Theorem. [br][br]Last, check to see if the triangles were all translated the same distance in the same direction. [br]13. Use the vector tool to connect lower left vertex of the dark blue triangle with the lower left vertex of the light blue triangle. [br]14. Use the move tool to move the vector from the lower left hand vertices to connect the lower right hand vertices. If it perfectly connects the lower right hand vertices, then the triangles moved the same distance in the same direction. [br]15. Move the vector around to see that all the triangles moved the same distance in the same direction.[br]