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Question
A Given AB = 3 cm, AC = 5 cm,and ∠B = 30°, ΔABC cannot be uniquely constructed, with AC as base, why?
A Given AB = 3 cm, AC = 5 cm,and ∠B = 30°, ΔABC cannot be uniquely constructed, with AC as base, why?
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Solution
The correct option is C The vertex B cannot be uniquely located.
The correct option is B The vertex B cannot be uniquely located.
The information of two sides and an angle is given, which means we could potentially draw a triangle.
using SAS criterion. However, SAS criterion requires the measurement of the included angle between the two sides which has a common vertex. But from the information provided,
∠B is given and the sides are AB and AC which means that ∠B is not the included angle. Hence we cannot construct a unique triangle with AC as the base.
The correct option is B The vertex B cannot be uniquely located.
The information of two sides and an angle is given, which means we could potentially draw a triangle.
using SAS criterion. However, SAS criterion requires the measurement of the included angle between the two sides which has a common vertex. But from the information provided,
∠B is given and the sides are AB and AC which means that ∠B is not the included angle. Hence we cannot construct a unique triangle with AC as the base.
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