A shape can be slid, flipped, or turned. Those are translation, reflection, and rotation.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
All three share one property.
Rigid motion is a move that changes a figure’s position but not its lengths or angles.
What does change
Only where the shape is, and which way it faces. Its size and shape are untouched.
Why this matters
Rigid motions are how congruence gets defined, and congruence is the whole of the next lesson.
Step 2: Try It Yourself
The dashed shape is the original. It stays so you can compare.
Every length and every angle is exactly as it was. The shape moved without changing, so the two figures are congruent.
Step 3: In Real Life
A phone screen
Rotate your phone and the photo turns; nothing in it changes. Drag an icon and it slides. Screens are built on rigid motions.
Step 4: Watch an Example
One step at a time.
Watch Ana Compare Before and After
Ana slides a triangle 4 units right.
- Step 1
She measures a side before: 5 units.
Step 5: Your Turn
Practice makes it stick.
The Slide
Problem 1 of 2
A point at (2, 5) is translated 3 right. What is its new first coordinate?
The Flip
Problem 2 of 2
A point at (4, 7) is reflected across the vertical axis. What is its new first coordinate?
Move It
1 of 4
(1, 3) translated 5 right. New first coordinate?
2 of 4
(6, 2) reflected across the vertical axis. New first coordinate?
3 of 4
(3, 8) reflected across the horizontal axis. New second coordinate?
4 of 4
Does a rigid motion change side lengths?
Step 6: Quick Check
Show what you know.
Question 1 of 2
(2, 9) reflected across the vertical axis. New first coordinate?
Question 2 of 2
What does a rigid motion preserve?
What You Learned
- Translation slides, reflection flips, rotation turns.
- All three keep every length and every angle.
- Only position and facing change.
For the grown-up
Three moves that preserve everything — A translation slides a figure, a reflection flips it across a line, and a rotation turns it about a point. All three leave every length and every angle exactly as it was. They are called rigid motions because the figure behaves like a solid object being moved.
What does change — Position changes; orientation may change. A reflected figure faces the other way, which matters for letters and for hands but not for lengths. Distinguishing what a move preserves from what it alters is the whole content of this chapter.
Describing a move precisely — A translation needs a direction and a distance. A reflection needs the mirror line. A rotation needs a center, an angle and a direction. Naming the move is not enough — a complete description lets someone else reproduce it exactly.
Try it with tracing paper — Trace a shape, then slide, flip or turn the tracing. Whatever you can do to the tracing without stretching it is a rigid motion. That physical test is a reliable check on whether a transformation preserves shape and size.
Trace it and move the tracing — Trace the triangle onto tracing paper. Slide the tracing across. Every side is still the same length. Flip it over. Still the same lengths and angles. Turn it. Still the same. Anything you can do to the tracing without stretching it is a rigid motion.