Ohio State Tests Geometry Congruence and Proof. Practice it free.

Every interior angle of a rectangle measures $90°$, so $3x-12=90$ and $x=34$.

A reflection is a rigid transformation that maps the points from a preimage, over a line of reflection, to the points of an image that are equidistant to the line. In this example, that line is the perpendicular bisector of a line segment from a point to its image, so the points map onto the same line segment, keeping the image the same.

The three interior angles sum to $180°$: $(x+8)+(2x+17)+(x+55)=180$, so $4x+80=180$ and $x=25$.

A rotation is a rigid transformation that turns a figure around a fixed point, called a center of rotation, by a specific angle in a specific direction. All points remain equidistant from the center of rotation, keeping the image congruent to the preimage. In this example, the image is congruent to the preimage and is located at a different angle around that center point.

Corresponding angles are congruent: $3x+16=2x+34$, so $x=18$. Each angle measures $3(18)+16=70°$.

A translation is a rigid transformation that moves every point of a figure the exact same distance in the same direction. Since all points in the image remain equidistant from the points in the preimage, the figure remains congruent. In this example, a point is never kept in the same place.

Same-side interior angles are supplementary: $(6x-5)+(4x+15)=180$, so $10x+10=180$ and $x=17$.

A rotation is a rigid transformation that turns a figure around a fixed point, called a center of rotation, by a specific angle in a specific direction. All points remain equidistant from the center of rotation, keeping the image congruent to the preimage.