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
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MultiChoice
Why is SSA (Side-Side-Angle) generally NOT a valid criterion for constructing a unique triangle?
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MultiChoice
Given side a = 5 cm, side b = 10 cm, and angle A = 30° opposite side a, how many triangles can be constructed?
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MultiChoice
Given side a = 3 cm, side b = 10 cm, and angle A = 30° opposite side a, how many triangles can be constructed?
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MultiChoice
Under what special condition does SSA result in exactly ONE unique triangle?
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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?
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MultiChoice
What is the SSA situation often called in geometry?
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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?
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MultiChoice
If angle A = 90°, side a (hypotenuse) = 10 cm, and side b = 6 cm, how many triangles can be constructed?
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MultiChoice
Which combination of given parts does NOT guarantee a unique triangle?
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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?
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MultiChoice
Given side a = 4 cm, side b = 8 cm, and angle A = 60° opposite side a, why can NO triangle be constructed?
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MultiChoice
In an SSA scenario, if the side opposite the given acute angle is strictly greater than the adjacent side, how many triangles exist?