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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.

Arizona Academic Standards learning standard: 8.G.B.6; 8.G.B.7 · the Pythagorean Theorem and its converse in problems in context

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 Arizona

In the Arizona Academic Standards, 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: Arizona Department of Education

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 48 cm and 20 cm. How long is the hypotenuse?

    answer boxcm

  2. Question 2

    The hypotenuse of a right triangle is 58 cm and one leg is 42 cm. How long is the other leg?

    answer boxcm

  3. Question 3

    A triangle has sides 3 cm, 4 cm and 7 cm. Is it a right triangle?

    • Yes
    • No

  4. Question 4

    A ladder leans against a wall. Its foot is 5 m from the wall and it reaches 12 m up the wall. How long is the ladder?

    answer boxm

  5. Question 5

    A rectangular field is 3 m by 4 m. How long is the diagonal across the field?

    answer boxm

  6. Question 6

    The legs of a right triangle are 7 cm and 9 cm. What is the hypotenuse, rounded to 1 decimal place?

    • 11.5 cm
    • 11.4 cm
    • 5.7 cm
    • 16.0 cm

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