Is It Right?

Learning Focus

Explain how rigid motions affect orientation and why right angles stay right.

Big idea

Orientation is the order (clockwise or counterclockwise) of a figure's vertices.

• Translations and rotations preserve orientation.
• Reflections reverse orientation (a mirror image).
• All rigid motions preserve angle measures, so a $90^\circ$ angle stays $90^\circ$.

Worked example

Triangle $ABC$ has sides $6,8,10$, so $6^2+8^2=10^2$ and it is a right triangle.

After any reflection, side lengths are still $6,8,10$, so the image is still a right triangle, though the vertex order now runs the opposite way.

Takeaways

• Reflection reverses orientation.
• Right angles remain right under rigid motions.
• Side lengths unchanged $\Rightarrow$ Pythagorean relation unchanged.