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8th grade · Math · Unit 3 of 17

Pythagorean Theorem

Right triangles and a² + b² = c²

What your child practices

Finding a missing side of a right triangle, checking whether a triangle is a right triangle, and using the theorem for ladders and diagonals.

Alabama Course of Study content standard: 8.26; 8.28 · the Pythagorean Theorem and its converse in real-world problems

How we explain it

Children can open this short lesson before they practice.

  1. It works for right triangles only.
  2. The two shorter sides (legs) are a and b. The longest side, across from the right angle, is c.
  3. a² + b² = c².

Example: A right triangle has legs 6 cm and 8 cm. How long is the longest side? 6² + 8² = 36 + 64 = 100. c = √100 = 10. Answer: 10 cm

Pythagorean Theorem in Alabama

In the Alabama Course of Study, this is unit 3 of 17 in 8th grade Math, after Patterns & Two-Step Equations and before Surface Area & Volume.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: Alabama State Department of Education (ALSDE)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    A right triangle has legs of 80 cm and 84 cm. How long is the hypotenuse?

    answer boxcm

  2. Question 2

    The hypotenuse of a right triangle is 34 cm and one leg is 30 cm. How long is the other leg?

    answer boxcm

  3. Question 3

    A triangle has sides 16 cm, 30 cm and 36 cm. Is it a right triangle?

    • Yes
    • No

  4. Question 4

    A ladder leans against a wall. Its foot is 15 m from the wall and it reaches 8 m up the wall. How long is the ladder?

    answer boxm

  5. Question 5

    A rectangular field is 40 m by 42 m. How long is the diagonal across the field?

    answer boxm

  6. Question 6

    The legs of a right triangle are 4 cm and 5 cm. What is the hypotenuse, rounded to 1 decimal place?

    • 9.0 cm
    • 3.0 cm
    • 6.4 cm
    • 6.5 cm

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