NJSLA Geometry Congruence. Practice it free.

A linear pair is supplementary: $(5x+10)+(3x+50)=180$, so $8x+60=180$ and $x=15$. The angles are $85°$ and $95°$, so the larger is $95°$.

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.

The three angles sum to $180°$: $2(65-x)+(4x+10)=180$, so $140+2x=180$ and $x=20$. Each base angle is $65-20=45°$.

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 segment maps onto itself.

The angles sum to $180°$: $(2x+5)+(3x+5)+(x+50)=180$, so $6x+60=180$ and $x=20$. The angles are $45°$, $65°$, and $70°$, so the largest is $70°$.

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, that angle is $80^{\circ}\textsf{.}$

Consecutive angles are supplementary: $(4x+6)+(2x+24)=180$, so $6x+30=180$ and $x=25$. Then $m\angle P=4(25)+6=106°$.

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, that distance is $6$ cm.