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8th grade · Math · Unit 3 of 19

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.

New York State Learning Standards learning standard: NY-8.G.6; NY-8.G.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 New York

In the New York State Learning Standards, this is unit 3 of 19 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: New York State Education Department (NYSED)

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

    answer boxcm

  2. Question 2

    The hypotenuse of a right triangle is 25 cm and one leg is 7 cm. How long is the other leg?

    answer boxcm

  3. Question 3

    A triangle has sides 5 cm, 12 cm and 14 cm. Is it a right triangle?

    • Yes
    • No

  4. Question 4

    A ladder leans against a wall. Its foot is 12 m from the wall and it reaches 16 m up the wall. How long is the ladder?

    answer boxm

  5. Question 5

    A rectangular field is 80 m by 84 m. How long is the diagonal across the field?

    answer boxm

  6. Question 6

    The legs of a right triangle are 2 cm and 4 cm. What is the hypotenuse, rounded to 1 decimal place?

    • 3.5 cm
    • 6.0 cm
    • 4.6 cm
    • 4.5 cm

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