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8th grade · Math · Unit 11 of 15

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.

Texas Essential Knowledge and Skills (TEKS) teks student expectation: 8.6(C); 8.7(C) · the Pythagorean Theorem and its converse

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 Texas

In the Texas Essential Knowledge and Skills (TEKS), this is unit 11 of 15 in 8th grade Math, after Surface Area & Volume and before Angle Detective.

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: Texas Education Agency (TEA)

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 12 cm and 16 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 60 cm, 63 cm and 87 cm. Is it a right triangle?

    • No
    • Yes

  4. Question 4

    A ladder leans against a wall. Its foot is 40 m from the wall and it reaches 42 m up the wall. How long is the ladder?

    answer boxm

  5. Question 5

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

    answer boxm

  6. Question 6

    The legs of a right triangle are 6 cm and 7 cm. What is the hypotenuse, rounded to 1 decimal place?

    • 9.2 cm
    • 13.0 cm
    • 9.3 cm
    • 3.6 cm

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