Problem 52
Question
Determine whether the statement is true or false. Justify your answer. If a triangle contains an obtuse angle, then it must be oblique.
Step-by-Step Solution
Verified Answer
True. According to the definitions of obtuse and oblique triangles, any triangle that includes an obtuse angle is not a right triangle and therefore must be an oblique triangle.
1Step 1: Define terms
The definitions of an obtuse angle and an oblique triangle are: an obtuse angle is an angle that measures more than 90 degrees, and oblique triangles are those triangles that are not right triangles, meaning they don't have a 90-degree angle.
2Step 2: Apply definitions
The statement 'If a triangle contains an obtuse angle, then it must be oblique.' implies that all triangles with an obtuse angle are also oblique triangles. According to the definition of obtuse and oblique triangles, this statement is true. Any triangle that includes an obtuse angle (i.e., an angle greater than 90 degrees) cannot also include a right angle, and so is not a right triangle. Therefore, it is an oblique triangle by definition.
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