The Pythagorean Theorem
Aligned to 8.G.B.7 — Common Core State Standards for Mathematics.
What this lesson teaches
In a right triangle, the squares of the two legs add up to the square of the hypotenuse: a² + b² = c². Use it to find a missing side.
Worked examples
Example 1
Legs 3 and 4: c² = 3² + 4² = 9 + 16 = 25, so c = √25 = 5.
Example 2
A ladder reaches 12 ft up a wall with its base 5 ft out. Its length: c² = 25 + 144 = 169, so c = 13 ft.
Example 3
To find a leg instead, subtract: if c = 10 and one leg is 6, then a² = 100 − 36 = 64, so a = 8. The hypotenuse is always the one alone on its side.
Practice questions
- Find the hypotenuse with legs 6 and 8.
- A ladder reaches 12 ft up a wall with its base 5 ft out. How long is it?
- If c = 13 and one leg is 5, find the other leg.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
El Teorema de Pitágoras
En un triángulo rectángulo, la suma de los cuadrados de los dos catetos es igual al cuadrado de la hipotenusa: a² + b² = c². Úsalo para encontrar el lado que falta.
Ejemplo 1: Catetos 3 y 4: c² = 3² + 4² = 9 + 16 = 25, entonces c = √25 = 5.
Ejemplo 2: Una escalera llega a 12 pies de alto en una pared con su base a 5 pies. Su longitud: c² = 25 + 144 = 169, así que c = 13 pies.
Ejemplo 3: Para hallar un cateto, resta: si c = 10 y un cateto es 6, entonces a² = 100 − 36 = 64, así que a = 8. La hipotenusa siempre es la que va sola en su lado.
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