L5 · Properties do not change: translations, rotations, reflections

Learning goal

“I can slide (translate), turn (rotate), and flip (reflect) a polygon, and I know its properties do not change: side lengths stay the same, angles stay the same, parallel sides stay parallel, and the distance between any two vertices stays the same.”

Translation — a slide: the shape moves to a new spot without turning or flipping, like a sliding door.

Rotation — a turn: the shape spins around a point, like a clock hand moving.

Reflection — a flip: the shape turns over, like a page being flipped or a pancake being tossed, making a mirror image.

Transformation — any of these moves: a slide, a turn, or a flip applied to a shape.

Worked example

Take a paper square. Slide it across the desk (a translation): it is in a new spot, but nothing about the shape changed - 4 equal sides, 4 right angles, 2 pairs of parallel sides. Now turn it (a rotation) until one corner points down, like a diamond. It LOOKS different. Check the properties anyway: sides - still 4, still all equal. Angles - test with the book corner: still 4 right angles. Opposite sides - still parallel; turning moved both sides of a pair together, so they still never meet. Say it plainly: a move changes where a shape is and which way it points. It never changes what the shape IS.

Check yourself — explain it

After the turn, one pair of the square's sides is slanted. Are those sides still parallel?

Paired problem — example still visible

A triangle with sides 5 cm, 6 cm, 7 cm is slid to the other side of the desk. What are its side lengths now? -> Still 5 cm, 6 cm, and 7 cm

Faded completion — last step is yours

"A rectangle is turned a quarter turn. Its right angles are still ___ angles." -> right

Ready to practise?

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

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