L5 · Verifying Properties with Transformations; Faces of Prisms

Learning goal

“I can use slides, flips, and turns to CHECK a shape's properties, I can tell a real polygon from a close approximation, and I can describe how the faces of a prism meet - parallel or perpendicular.”

Slide (translation) — moving a shape to a new place without turning or flipping it. The shape looks exactly the same, just somewhere else.

Flip (reflection) — turning a shape over, like a page, so it faces the other way - a mirror image.

Turn (rotation) — spinning a shape around a point, like a clock hand moving.

Face — one flat surface of a solid (3-D) shape. A box has 6 faces.

Worked example

Take a paper triangle with sides 4 cm, 5 cm, 6 cm. Step 1 (slide): Slide it across the desk. Measure again: 4, 5, 6. A slide changes the PLACE, never the properties. Step 2 (flip): Flip it over. Measure again: 4, 5, 6. A flip changes which way it faces, never the lengths or angles. Step 3 (turn): Turn it half a turn. Same measures again. Slides, flips, and turns never change a shape's side lengths or angle sizes - that is exactly why they are perfect checking tools: lay a copy of one side on top of another side (slide it over); if they match exactly, the sides are equal - proven, not guessed. Step 4 (the fake): Now a drawn "square" whose measured sides are 6 cm, 6 cm, 6 cm, 5 cm. It resembles a square, but a square's defining property is ALL sides equal - 5 is not equal to 6, so this is a close approximation of a square, not a square. Resembling is not being.

Check yourself — explain it

Why does sliding a paper copy of a side onto another side PROVE the sides are equal?

Paired problem — example still visible

A shape with sides 3 cm, 4 cm, 5 cm is flipped over. What are its side lengths after the flip? -> 3 cm, 4 cm, 5 cm - unchanged

Faded completion — last step is yours

"A turn can change a shape's position, but it can never change its side ___ or its angle ___" -> lengths; sizes

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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