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🔺 8th grade math · Shapes & Space

The Pythagorean theorem

In a right triangle, the legs a and b and the long side c (hypotenuse) fit a² + b² = c². 3² + 4² = 25 and 5² = 25. For a missing leg, subtract: c² − a² = b².

Worked example

Find the length of the side marked ?. (in in)
12 in5 in?
Answer: 13
a² + b² = c². 12² + 5² = 169, so c = √169 = 13 in. Answer: 13.

For grown-ups: Pythagorean theorem and converse; distance. Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.

  • CCSS 8.G.B.6–8
What this practises, for teachers

Practices pythagorean theorem and converse; distance (8.G.B.6–8). A printable sheet with its answer key, worked answers on the page, no accounts.

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For your class

🖨️ Printable sheet and key

On the board with this skill:

Try three

  1. Find the length of the side marked ?. (in km)
    4 km3 km?
    Show the answer and how
    Answer: 5
    a² + b² = c². 4² + 3² = 25, so c = √25 = 5 km. Answer: 5.
  2. Find the length of the side marked ?. (in cm)
    5 cm?13 cm
    Show the answer and how
    Answer: 12
    a² + b² = c², so the missing leg² = c² − the known leg². 13² − 5² = 169 − 25 = 144, so the leg is √144 = 12 cm. Answer: 12.
  3. Find the length of the side marked ?. (in km)
    12 km?13 km
    Show the answer and how
    Answer: 5
    a² + b² = c², so the missing leg² = c² − the known leg². 13² − 12² = 169 − 144 = 25, so the leg is √25 = 5 km. Answer: 5.

Before and after

Learn first: Slide, flip, turn, stretch (8th)

Name: ____________________Date: ____________Score: ____ / 12

The Pythagorean theorem (8th grade)

  1. Find the length of the side marked ?. (in km)
    9 km12 km?
  2. Find the length of the side marked ?. (in yd)
    15 yd8 yd?
  3. Find the length of the side marked ?. (in ft)
    5 ft12 ft?
  4. Find the length of the side marked ?. (in m)
    15 m8 m?
  5. Find the length of the side marked ?. (in m)
    6 m8 m?
  6. Find the length of the side marked ?. (in cm)
    ?8 cm17 cm
  7. Find the length of the side marked ?. (in cm)
    3 cm?5 cm
  8. Find the length of the side marked ?. (in cm)
    15 cm?17 cm
  9. Find the length of the side marked ?. (in yd)
    16 yd?20 yd
  10. Find the length of the side marked ?. (in cm)
    8 cm?17 cm
  11. Find the length of the side marked ?. (in yd)
    8 yd15 yd?
  12. Find the length of the side marked ?. (in cm)
    15 cm20 cm?

Answer key

  1. 15
  2. 17
  3. 13
  4. 17
  5. 10
  6. 15
  7. 4
  8. 8
  9. 12
  10. 15
  11. 17
  12. 25

More 8th grade skills: all 8th grade math skills, or every grade at math skills.