L26 · Pythagorean theorem and its converse

1. 1.

   A right triangle has legs 6 and 8. What is the hypotenuse?

   Answer. 10

   6² + 8² = 100 = 10².

2. 2.

   Is a triangle with sides 8, 15, 17 a right triangle?

   Answer. yes

   Check 8² + 15² = 17².

3. 3.

   Is a triangle with sides 8, 15, 17 a right triangle?

   Answer. yes

   Check 8² + 15² = 17².

4. 4.

   Is a triangle with sides 7, 24, 25 a right triangle?

   Answer. yes

   Check 7² + 24² = 25².

5. 5.

   A right triangle has legs 5 and 12. What is the hypotenuse? Then Priya needs 5 of that amount. What is the total they need?

   Answer. 65

   5² + 12² = 169 = 13². Then multiply by 5: 65.

6. 6.

   Is a triangle with sides 9, 12, 15 a right triangle? Write a complete answer — Mei will compare with a partner.

   Answer. yes

   Check 9² + 12² = 15².

7. 7.

   Is a triangle with sides 9, 12, 15 a right triangle? Write a complete answer — Theo will compare with a partner.

   Answer. yes

   Check 9² + 12² = 15².

8. 8.

   A right triangle has legs 3 and 4. What is the hypotenuse? Then Mei needs 2 of that amount. What is the total they need?

   Answer. 10

   3² + 4² = 25 = 5². Then multiply by 2: 10.

9. 9.

   A right triangle has legs 5 and 12. What is the hypotenuse? Then Mei needs 4 of that amount. What is the total they need?

   Answer. 52

   5² + 12² = 169 = 13². Then multiply by 4: 52.

10. 10.

    A right triangle has legs 8 and 15. What is the hypotenuse? Then Nora needs 3 of that amount. What is the total they need?

    Answer. 51

    8² + 15² = 289 = 17². Then multiply by 3: 51.

11. 11.

    Think

    Nora tried this problem:
    Is a triangle with sides 3, 4, 5 a right triangle?
    Nora wrote no. That is not correct. What is the right answer?

    Answer. yes

    Nora’s answer no is off. Check 3² + 4² = 5².

12. 12.

    Think

    Ava tried this problem:
    A right triangle has legs 9 and 40. What is the hypotenuse?
    Ava wrote 82. That is not correct. What is the right answer?

    Answer. 41

    Ava’s answer 82 is off. 9² + 40² = 1681 = 41².

Original extra practice. Keys are computed from the items, not guessed.