Congruence & Invariance — The Unchanging
⚙ Congruence Scanner
📡 Logic Track
If you can cut it out and place it exactly on top of the other — same size, same shape — they are congruent.
A reflection flips the shape across a mirror line. Every length and angle is perfectly preserved. The image is the mirror twin of the original.
Points lying ON the mirror line do not move — they are invariant.
Two shapes are congruent if one can be placed exactly on top of the other — same shape, same size. Translations, reflections, and rotations always produce congruent images.
An invariant point is a point that does NOT move under a transformation. During a reflection, any point lying exactly ON the mirror line is invariant. During a rotation, only the centre of rotation is invariant.
Enlargements with scale factor k ≠ 1 produce SIMILAR shapes — not congruent. Corresponding angles remain equal, but lengths scale by k. Only when k = 1 (or k = −1) does the image remain congruent.
🧮 Dynamic Solver — Invariant Finder
Do NOT say the entire mirror line is invariant. Only the vertices of the original shape that sit on y = 1 are invariant points.
Reflection, Rotation, Translation all preserve every length and angle. The image is an exact copy.
Enlargement (k ≠ 1) preserves angles but scales lengths. Shapes are similar — proportional but not identical.
A point is invariant if its image coincides with itself. In a reflection: points ON the mirror line. In a rotation: only the centre.
Sign In to Keep Going
You've reached the end of the free preview. Sign in — and upgrade to Plus or Pro — to keep going with Math4MA1.
Full Access
Unlock all 158 lessons