Pythagoras & TransformationsThe theorem, its converse, distance formula, and the four…8th GradeTHE PYTHAGOREAN THEOREMbaca² + b² = c²c is the hypotenuse — opposite the right angle.Find the hypotenuse: c = √(a² + b²)Find a leg: a = √(c² − b²)Triples worth knowing: 3-4-5 · 5-12-13 · 8-15-17 · 7-24-25THE CONVERSE & THE DISTANCE FORMULAIf a² + b² = c², the triangle is right-angled. If a² + b² > c² it is acute; if less, obtuse.d = √[(x₂ − x₁)² + (y₂ − y₁)²]— Pythagoras on the gridTRANSFORMATIONSTranslationslide(x, y) → (x + a, y + b)same size, same shapeReflectionflipover x-axis: (x, −y) · over y-axis: (−x, y)same size, mirroredRotationturn90° about origin: (x, y) → (−y, x)same size, turnedDilationresize(x, y) → (kx, ky)similar, not congruentThe first three keep congruence. Only dilation changes size.Pythagoras & Transformationswww.littleactivity.com

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Math · 8th Grade

Pythagoras & Transformations

The theorem, its converse, distance formula, and the four transformations.

How to use it

Label the hypotenuse before writing anything else down.

Free · print-ready PDF · US Letter and A4

Grade
8th Grade
Ages
13–14
Subject
Math
Pages
1

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