L29 · Figures with given conditions

1. 1.

   Two sides of a triangle are 5 cm and 8 cm. The included angle is 40°. Is this triangle unique?

   Answer. yes (SAS)

   Two sides and the included angle determine a unique triangle (SAS).

2. 2.

   Can a triangle have side lengths 6, 6, and 14?

   Answer. no

   Triangle inequality: 6 + 6 = 12 ≤ 14.

3. 3.

   Can a triangle have side lengths 6, 5, and 8?

   Answer. yes

   Triangle inequality: 6 + 5 = 11 > 8.

4. 4.

   Two sides of a triangle are 5 cm and 8 cm. The included angle is 40°. Is this triangle unique?

   Answer. yes (SAS)

   Two sides and the included angle determine a unique triangle (SAS).

5. 5.

   Two sides of a triangle are 5 cm and 8 cm. The included angle is 40°. Is this triangle unique? Write a complete answer — Priya will compare with a partner.

   Answer. yes (SAS)

   Two sides and the included angle determine a unique triangle (SAS).

6. 6.

   Two sides of a triangle are 5 cm and 8 cm. The included angle is 40°. Is this triangle unique? Write a complete answer — Owen will compare with a partner.

   Answer. yes (SAS)

   Two sides and the included angle determine a unique triangle (SAS).

7. 7.

   Can a triangle have side lengths 3, 6, and 14? Write a complete answer — Grace will compare with a partner.

   Answer. no

   Triangle inequality: 3 + 6 = 9 ≤ 14.

8. 8.

   Two sides of a triangle are 5 cm and 8 cm. The included angle is 40°. Is this triangle unique? Write a complete answer — Owen will compare with a partner.

   Answer. yes (SAS)

   Two sides and the included angle determine a unique triangle (SAS).

9. 9.

   Can a triangle have side lengths 4, 4, and 8? Write a complete answer — Mei will compare with a partner.

   Answer. no

   Triangle inequality: 4 + 4 = 8 ≤ 8.

10. 10.

    Can a triangle have side lengths 5, 5, and 10? Write a complete answer — Grace will compare with a partner.

    Answer. no

    Triangle inequality: 5 + 5 = 10 ≤ 10.

11. 11.

    Think

    Nora tried this problem:
    Two sides of a triangle are 5 cm and 8 cm. The included angle is 40°. Is this triangle unique?
    Nora wrote yes (SAS) (check this). That is not correct. What is the right answer?

    Answer. yes (SAS)

    Nora’s answer yes (SAS) (check this) is off. Two sides and the included angle determine a unique triangle (SAS).

12. 12.

    Think

    Elena tried this problem:
    Two sides of a triangle are 5 cm and 8 cm. The included angle is 40°. Is this triangle unique?
    Elena wrote yes (SAS) (check this). That is not correct. What is the right answer?

    Answer. yes (SAS)

    Elena’s answer yes (SAS) (check this) is off. Two sides and the included angle determine a unique triangle (SAS).

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