Learning Takeaways: After this lesson, students will be able to:
Two figures are congruent if they are the:
Look at the example below.
These triangles are congruent. They are the exact same size AND shape. If you slid triangle A to the right, it would exactly cover triangle B. This is called a translation. You will learn more about translations in the next section of this lesson. 
These rectangles are not congruent. They are not the same size.  
These triangles are not congruent. They are the same size but not the same shape. Triangle B is a right triangle. Triangle A is an isosceles triangle.  
Are these two parallelograms congruent? Are they the exact same shape and the exact same size? Answer: They are the same shape and size so they are congruent. See more about rotations later in this lesson.  
Which figure is congruent to figure C shown below?  
Figure b. is congruent. 
There are three types of transformations. Alternative names are in parenthesis:
Rotations, reflections, and translations are isometric. That means that these transformations do not change the size of the figure. If the size and shape of the figure is not changed, then the figures are congruent.
Examples of Transformations  
Rotation 
Triangle A is a 90° rotation of triangle B. The angle of rotation of is 90 degrees. Notice how the angle created between the 2 figures is equal to the angle of rotation. 
Reflection 
Reflections “flip” a figure over a line (often referred to as a line of symmetry). Reflections are mirror images and appear “backwards” from the original figure. 
Translation 
A translation slides or glides a figure from one place to another. A translation cannot have any rotation (or else it would be a rotation). 
Recapping from earlier in his lesson, there are three types of transformation:
Two Transformations  

Triangle B has performed two transformations. It is rotated 90° and translated. Triangle B is a rotation of triangle A because it turned 90°. It was also slid up and to the right, making a translation. 

What two transformations could have been performed here? Hint: Figure 2 is a mirror image of figure 1. Figure 2 is a reflection and translation of figure 1. The figure is a reflection because it flipped. It is a translation because it is moved to another place, without rotating it. This is also called a glide reflection. 
Think: Does figure Z face the same direction? Are corresponding parts of the parallelogram parallel each other? Are the figures in the same quadrant of the Cartesian plane? 