Final answer:
After proving triangle congruence, the next move could be to find unknown angles or side lengths using congruent properties, the Pythagorean theorem, or trigonometric relationships, depending on what the problem asks for.
Step-by-step explanation:
After proving the congruence of triangle GEF and triangle ADH, the next move to solve this problem depends on what you are trying to find. If the goal is to find specific lengths or angles within the triangles, you might:
- Find the angles of triangle GEF if they are not already known, as congruent triangles have equal corresponding angles.
- Find the lengths of the sides of triangle ADH using the congruent sides from triangle GEF, as congruent triangles also have equal corresponding sides.
- Use the Pythagorean theorem if the triangles are right-angled, to find the unknown sides, given that one of the sides and the hypotenuse or both sides are known.
- Use trigonometric relationships such as the sine, cosine, or tangent ratios to find unknown angles or sides, especially when dealing with non-right angled triangles.
If the primary objective is to continue proving congruence or relationships between other triangles or lines within a geometric configuration, you might prove another pair of triangles congruent.
Therefore, the next step is based on what information is missing or what the problem is asking you to solve for. If the problem is to find unknown angles or sides within the congruent triangles, applying appropriate mathematical principles like the Pythagorean theorem or trigonometry would be necessary.