What is the sequence of steps used to move the triangle and quadrant for to the triangle and quadrant 2 to show that the triangles are congruent
To show that two triangles are congruent, typically we use the concept of rigid transformations. In this case, the steps to move Triangle 1 to Triangle 2 would be as follows:
1. Start by placing Triangle 1 and Triangle 2 so that their corresponding sides are parallel and their corresponding angles are congruent. This initial position allows us to compare the triangles and determine how to transform one into the other.
2. Perform a translation: Choose a vector (a movement of a given distance and direction) to shift Triangle 1 to Triangle 2. The distance and direction should align the corresponding vertices of both triangles.
3. Perform a rotation: Choose an angle to rotate Triangle 1. The angle should be such that the side that is not corresponding aligns with the side of Triangle 2 that is not corresponding. This rotation ensures that all corresponding angles are congruent.
4. Perform a reflection: Choose a line of reflection that can mirror Triangle 1 onto Triangle 2. The line of reflection should pass through the midpoint of the corresponding side of both triangles.
By performing these three transformations (translation, rotation, and reflection) in the correct order, Triangle 1 can be moved and correctly superimposed onto Triangle 2, thereby showing that the triangles are congruent.