Form 7: The Ambiguous Case and SSA Condition Exercise

Form 7: The Ambiguous Case and SSA Condition

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Form 7: The Ambiguous Case and SSA Condition

Examine the Side-Side-Angle condition and explore the ambiguous case in triangle construction. Determine when SSA information results in zero, one, or two triangles.

Questions

  1. MultiChoice

    Why is SSA (Side-Side-Angle) generally NOT a valid criterion for constructing a unique triangle?

  2. MultiChoice

    Given side a = 5 cm, side b = 10 cm, and angle A = 30° opposite side a, how many triangles can be constructed?

  3. MultiChoice

    Given side a = 3 cm, side b = 10 cm, and angle A = 30° opposite side a, how many triangles can be constructed?

  4. MultiChoice

    Under what special condition does SSA result in exactly ONE unique triangle?

  5. MultiChoice

    If side a = 8 cm, side b = 6 cm, and angle A = 40° (opposite the longer side a), how many triangles can be formed?

  6. MultiChoice

    What is the SSA situation often called in geometry?

  7. MultiChoice

    When constructing a triangle with sides 12 cm and 8 cm and a 30° angle opposite the 8 cm side, how many intersection points can the arc make with the baseline?

  8. MultiChoice

    If angle A = 90°, side a (hypotenuse) = 10 cm, and side b = 6 cm, how many triangles can be constructed?

  9. MultiChoice

    Which combination of given parts does NOT guarantee a unique triangle?

  10. MultiChoice

    Why does SSA fail to guarantee uniqueness when the side opposite the acute angle is shorter than the adjacent side but longer than the height?

  11. MultiChoice

    Given side a = 4 cm, side b = 8 cm, and angle A = 60° opposite side a, why can NO triangle be constructed?

  12. MultiChoice

    In an SSA scenario, if the side opposite the given acute angle is strictly greater than the adjacent side, how many triangles exist?