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.
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 centre, 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.
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: 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 4: 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 5: 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.