What is the sequence of transformations needed to move triangle abc to triangle egh to show that the triangles are congruent?
To show that triangle ABC is congruent to triangle EGH, we need to perform a sequence of transformations. Here is one possible sequence of transformations:
1. Translation: Move triangle ABC to a new location. Choose a vector that will move point A to point E. Let's say we need to move it 5 units to the right and 2 units up. So, we translate triangle ABC by the vector (5, 2).
2. Rotation: Rotate triangle ABC around point E to align it with triangle EGH. The angle of rotation will depend on the relationship between sides and angles of the triangles. Let's say we need to rotate it 90 degrees counterclockwise.
3. Reflection: Reflect the rotated triangle about a line to align it with triangle EGH. The line of reflection could be any line of symmetry between the two triangles. Let's say we choose the line that passes through points E and G.
By performing these three transformations (translation, rotation, and reflection), triangle ABC will be transformed into triangle EGH, showing that they are congruent.